A sitting president can't be arrested because everyone with the power to arrest at the federal level is subordinate to the president. Arrest is a strictly executive function. The president even controls the marshals.
"High crimes and misdemeanors" was cleanly but subtly defined by Tocqueville as acts of mischief which aren't forbidden by law. I don't have the exact quote. You can also call it a general failure to meet fiduciary duty. If Congress merely suspects the president is an asshole, that is sufficient grounds for impeachment.