Yeah, the Electoral College has turned into 1) a rubber stamp of approval and 2) a way for politicians to gerrymander the vote (and republicans are better at this than democrats). It's so laughable when people scream for electors to "do their duty" to vote the way the state voted. That's not their duty at all
Correct. The main problems with the Electoral College are a) the winner-takes-all system, and b) the appointment of electors who are hardcore party loyalists. IIRC, Madison was firmly against the latter, as he favored the idea of an educated, intellectual elite who would serve as a check on the will of the uneducated voting masses. As far as winner-takes-all, it was intended to ensure that there was always a clear victor at the national level, and to prevent the diffusion of state power. Like, if all of the electors for big state #1 vote the same way, then if all of the electors of state #2 aren't united and don't do the same, then their voice gets overwhelmed by state #1. Personally, I think it's a pretty dumb thing to be concerned with, and the combination of a) and b) leads to unreasonably lopsided results in the electoral college when the national race is very close in a number of the larger states.
The third issue I have with the electoral college is more of a matter of opinion, which is how voters in less populated states are given greater power on a per-vote basis than voters in more populous states. Some people think this is a great idea -- we are a republic, after all, and not a pure democracy. Personally, I favor a strong federal government with weaker state governments. I don't think any single person's vote should count more than anyone else's either.
Depends on how badly Republicans feel Trump will damage their long-term image and American international relations.
This is the key. Remember that the Republicans expected to lose big time going into this election, and most were just as surprised as the rest of us that Trump won. However, most Republican politicians are party loyalists first, and everything else second. They will stand by Trump even through major controversies and even while he deviates from Republican norms or simple common sense, making public condemnations of his actions while still voting to support him. Just pay attention to the news and you'll see this is already happening. Republicans will only turn on Trump in large numbers if Trump's supporters among the voters turn on him first, because those are the same voters that put those Republicans in office in the first place.