Not since Eugene V. Debs campaigned from a prison cell more than a century ago has the United States experienced what is now happening: a prominent candidate with felony convictions running for president. And never before has that candidate been someone with a real chance of winning.

A Manhattan jury convicted former President Donald J. Trump on Thursday of falsifying business records to cover up a hush-money payment to a porn star. He has been charged with dozens of other felonies across three additional cases: two federal and one in Georgia.

For now, he faces no formal campaign restrictions, and he remains highly competitive in polls. But his sentencing on the New York convictions is approaching, on July 11, the other cases are still looming, and the Constitution and U.S. law have clear answers for only some of the questions that have arisen and may still arise.

Others could bring the country into truly uncharted territory, with huge decisions resting in the hands of federal judges.

Here is what we know, and what we don’t know.

Can Trump still run after his conviction?

This is the simplest question of the bunch. The answer is yes.

The Constitution sets very few eligibility requirements for presidents. They must be at least 35 years old, be “natural born” citizens and have lived in the United States for at least 14 years.

There are no limitations based on character or criminal record. While some states prohibit felons from running for state and local office, these laws do not apply to federal offices.

The Republican and Democratic Parties have guaranteed spots on general-election ballots in every state, and the parties tell election officials whose name to put in their spot. States could, in theory, try to keep Mr. Trump off the ballot by passing legislation requiring a clean criminal record, but this would be on legally shaky ground.

“We let states set the time, place and manner” of elections, said Jessica Levinson, a professor at Loyola Law School who specializes in election law, “but I think the best reading of our Constitution is you don’t let the state add new substantive requirements.”

While that view is not universal among legal experts, it prevailed in court in 2019, after California passed a law requiring candidates to release their tax returns in order to appear on primary ballots. A federal district judge blocked the law from taking effect, saying it was most likely unconstitutional. The California Supreme Court also unanimously blocked it as a violation of the state’s Constitution, and the case never reached the U.S. Supreme Court.

What about the 14th Amendment?

The Supreme Court ruled unanimously in March that states could not keep Mr. Trump off their ballots under Section 3 of the 14th Amendment, which disqualifies people who “engaged in insurrection or rebellion” after taking an oath to support the Constitution.

Numerous lawsuits had argued that Mr. Trump’s actions before and on Jan. 6, 2021 — which are the subject of two criminal cases against him, but not the one in which he was convicted — met this bar. In December, the Colorado Supreme Court found him ineligible, and Maine’s secretary of state did the same.

But the Supreme Court — led by a conservative supermajority, with three justices appointed by Mr. Trump himself — concluded that only Congress had the power to enforce Section 3 against candidates for federal office. (Four of the justices, including the three liberals, wanted to allow a wider range of options for disqualification.)

Congress is not going to do that with Republicans in control of the House. And the 14th Amendment is separate from criminal cases, meaning convictions in the election-related cases would not disqualify Mr. Trump either.

Congress can designate either groups of people to whom Section 3 applies (such as people who fought for the Confederacy) or specific crimes that, upon conviction, would prompt disqualification, said Anthony Michael Kreis, an assistant professor of law at Georgia State University. But none of the crimes Mr. Trump is charged with carry that automatic penalty.

“Whether or not Trump is tried, convicted, acquitted, that’s a separate question from whether or not he’s disqualified,” said Richard L. Hasen, an election law expert at the University of California, Los Angeles.

One of the charges in the federal case related to Mr. Trump’s efforts to overturn the 2020 election — conspiracy to violate civil rights — once carried a disqualification penalty, Mr. Kreis said, but Congress removed it decades ago.

Could the party replace him on the ticket?

Now that Mr. Trump has secured a majority of delegates to the Republican convention, the party has no mechanism to nominate somebody else. Under the party’s official convention rules, if a delegate tries to support someone other than the person the primary results bound them to, “such support shall not be recognized.”

Nor have top Republicans shown any interest in another nominee.

If he were forced to withdraw from the race after the convention, party leaders could replace him then; they considered doing so in 2016 after the release of the “Access Hollywood” tape in which he bragged about grabbing women’s genitals. But this is highly unlikely given how vigorously the party has circled the wagons around him.

Can he vote after his conviction?

It depends on his sentence. Here’s what we know:

Mr. Trump is registered to vote in Florida, and people convicted of felonies are disenfranchised there. Most felons in Florida regain voting rights after completing their full sentence, including parole or probation, and paying all fines and fees. But depending on what the sentence is, Mr. Trump may not have time to complete it before Election Day.

New York’s rules are somewhat more lenient: Felons there can vote while on parole or probation. And there is a chance that if New York would let Mr. Trump vote, then Florida will too. There’s a provision in Florida law that might apply New York’s standards, because that’s where the conviction happened. A spokesman for the Florida secretary of state’s office did not immediately respond to inquiries on Thursday about that provision.

But, as in Florida and almost every other state, felons in New York are still disenfranchised while in prison — so if Mr. Trump is imprisoned, he would be disenfranchised regardless. That would put him in the extraordinary position of being deemed fit to be voted for, but unfit to vote.

He could petition for clemency, which would require the approval of Florida’s governor — Ron DeSantis, who ran against Mr. Trump in the Republican primary — and two Florida cabinet members. Chris Taylor, the director of external affairs for the Florida Commission on Offender Review, confirmed that Florida residents convicted of a felony could apply to have their voting rights restored through that process even if their conviction happened outside Florida.

What happens if Trump is elected from prison?

No one knows.

“We’re so far removed from anything that’s ever happened,” said Erwin Chemerinsky, a constitutional law expert at the University of California, Berkeley. “It’s just guessing.”

Legally, Mr. Trump would remain eligible to be president even if he were imprisoned. The Constitution says nothing to the contrary. “I don’t think that the framers ever thought we were going to be in this situation,” Professor Levinson said.

In practice, the election of an incarcerated president would create a legal crisis that would almost certainly need to be resolved by the courts.

In theory, Mr. Trump could be stripped of his authority under the 25th Amendment, which provides a process to transfer authority to the vice president if the president is “unable to discharge the powers and duties of his office.” But that would require the vice president and a majority of the cabinet to declare Mr. Trump unable to fulfill his duties, a remote prospect given that these would be loyalists appointed by Mr. Trump himself.

More likely, Mr. Trump could sue to be released on the basis that his imprisonment was preventing him from fulfilling his constitutional obligations as president.

If he were convicted in one of the two federal cases before the election — an increasingly unlikely prospect, given his lawyers’ success in delaying both of those cases — and then won in November, he could also try to pardon himself or to commute his sentence after getting into office. That would leave his conviction in place but end his imprisonment. Either action would be an extraordinary assertion of presidential power, and the Supreme Court would be the final arbiter of whether a “self pardon” was constitutional.

Or President Biden, on his way out the door, could pardon Mr. Trump on the basis that “the people have spoken and I need to pardon him so he can govern,” Professor Chemerinsky said.

But a presidential pardon is not an option in relation to the New York case, and would not be in the Georgia case either, because the president does not have pardon power for state charges.

What if he’s elected with cases still in progress?

In the two federal cases, most likely, a Trump-appointed attorney general would withdraw the charges.

The Justice Department does not indict sitting presidents, a policy outlined in a 1973 memo, during the Nixon era. It has never had reason to develop a policy on what to do with an incoming president who has already been indicted. But the rationale for not indicting sitting presidents — that it would interfere with their ability to perform their duties — applies just as well in this hypothetical scenario.

“The reasons why we wouldn’t want to indict a sitting president are the reasons we wouldn’t want to prosecute a sitting president,” said Professor Chemerinsky, who has disagreed with the department’s reasoning. “My guess is, if the Trump prosecution were still ongoing in some way and Trump were elected, the Justice Department — which would be the Trump Justice Department — would say, ‘We’re following the 1973 memo.’”

Like so much else here, this would be legally untested, and it is impossible to say what the Supreme Court would do if the question reached it.

What would happen to the Georgia case, a state criminal proceeding beyond the reach of a Trump-run Justice Department, is a harder question still — one the country has never had reason to develop a road map for.

In its Clinton v. Jones ruling in 1997, the court allowed a lawsuit against President Bill Clinton to proceed. But that case was civil, not criminal, and it was filed by a private citizen, not by the government itself.