Treason does not require that an act of war take place.
Having said that, it's generally accepted that indicting a sitting president on criminal charges and trying him in court is unconstitutional. That's why the Constitution provides for impeachment - which is the political version of an indictment - and a trial in the Senate. So, at least while he's president, Trump can't be "charged" (criminally) with anything. He would have to be impeached. Article 2, Section 4 of the US Constitution says that "The President ... shall be removed from Office on Impeachment for, and Conviction of, Treason, Bribery, or other high Crimes and Misdemeanors." My understanding is that it's a bit of an open question whether, once impeached and removed from office, criminal charges could then be brought against the (now) former president for whatever crimes were committed.
As I said above, impeachment is a political process. It's for the House and Senate to impeach and convict (or not.) Politicians will be looking to respond to their constituents and save their prospects of re-election. Nixon resigned because impeachment and conviction became inevitable. It's reported that a few days before he resigned, a group of Republican members of Congress told him that impeachment in the House was a certainty and that he had no more than 15 votes for acquittal in the Senate. (He would have needed 34.) So he resigned rather than going through a process that he couldn't win. Republicans turned on Nixon because Nixon was dragging them down. He hadn't lost Congress - he had lost his political base of support, and because of that Congress (even the Republicans) turned on him. That hasn't happened with Trump. His core seems to be absolutely rock solid. His core is convinced that this is all just a giant conspiracy by Clinton supporters, the establishment, and even the Republican elite to get rid of him. His core isn't the traditional Republican core, but Republicans in Congress are going to need that core to get re-elected. As long as Trump's core vote holds firm, it's hard to see him being impeached and removed.
As for what would happen after Trump leaves office, Richard Nixon was never impeached, but he was pardoned by Gerald Ford, which suggested that Ford at least believed that former presidents could be charged with crimes they committed while in office. So, perhaps, after Trump leaves office in 2021 or 2025 (if he serves a full 4 or 8 years) a criminal indictment might be possible. But if he were to be impeached and removed from office then would indictment and trial in a court after being removed on impeachment and by trial in the Senate be considered a form of double jeopardy, I wonder? It's never happened, so we have no way of knowing.