If you mean the first president who chose not to go to war, no he's not. Clinton and GW Bush also chose not to participate in Vietnam. Clinton got educational deferments. Bush got into the Texas Air Nat'l Guard (ahead of a long waiting list) where they spent a million dollars teaching him to fly, then he quit before his commitment was up when he found something else he'd rather do.
But Congress is FULL of what we call 'chicken hawks'--politicians who praised the Vietnam War but decided they had better things to do themselves (and their sons also). The great majority of these are Republicans, of course. Republicans leaders never saw a war they didn't like, but THEY didn't fight in them.
No. Many draft dodgers were elected POTUS. However, Trump is not a draft dodger because he wasn't eligible for the draft for medical reasons and didn't do anything to dodge it.
No. Clinton didn't serve. G.W claims to have been in the National Guard, but no one saw him there. The children of the rich and the upper middle class for the most part did not serve in Vietnam- there were ways of getting exemptions. Whether Bush's dubious service was more honorable than Clinton and Trump using deferments is for you to judge. I don't personally think it matters. One does not have to have been a soldier to be a good president.