She cannot be "convicted" of anything so long as she's in office. She would have to be impeached and removed from office (or resign) before she could actually stand trial for whatever crime may have been committed.
There is a lot of historical precedent. A US President can generally claim immunity to everything except an impeachment. Regardless of laws, you'd never find someone capable of arrest the US President. Secret service would quickly fill anyone attempting to do so with bullets. Worst case scenario, the President can go hang out at a military base of which he or she has absolute authority. Good luck having the DC Police SWAT one of those.
A little googling and it turns out you are almost right. The Sergent at Arms of the US Senate can arrest anyone who violates Senate rules, including the president.
I have no idea if the emails are related enough, as I don't have voting rights in the US I see no reason to care about them.
I believe the House of Representatives brings articles of impeachment, not the Senate, and the House will likely hold its Republican majority.
The Senate is only required to actually convict. It's pretty much a disaster simply to be impeached at all. No conviction is really necessary to permanently damage someone politically.