Only registered Republicans are allowed to vote, except in those states that allow open primaries. Illegal voters get turned over to the proper authorities. These are my predictions for the ones running.
When a sitting president receives a challenge, he either loses the general, withdraws which the new nominee loses the general. I have no idea if Trump will choose to run again or not. One thing is for certain, I will never vote for him. History of sitting presidents who were challenged.
1952 Estes Kefauver challenged Truman and beat Truman in the New Hampshire primary. Truman withdrew. But Stevenson won the nomination and lost to Eisenhower.
1968 Eugene McCarthy challenged LBJ and lost narrowly to LBJ in the New Hampshire primary. LBJ withdrew, Humphrey would become the Democratic nominee only to lose to Nixon in the general election.
1976 Ronald Reagan challenged Ford, Ford prevailed, but lost to Jimmy Carter in the general election.
1980 Teddy Kennedy challenged Carter, Carter prevailed, but lost to Reagan in the general election.
1992 Pat Buchanan challenged G.H.W. Bush, Bush prevailed, but lost to Bill Clinton in the general election.
Whenever a sitting president is challenged, he loses or his party nominee loses the presidential election. If Trump decides to run for reelection in 2020 and is challenged by Kasich, Rubio, Flake and or someone else, he'll lose the general or whomever receives the Republican nomination will lose the general. Even if Trump isn't challenged, unless the Democrats nominate another Hillary Clinton, we'll have a Democratic president after 2020.