Correct. They use their judgement to vote in ways that (in their view) are for the best for their constituents. That isn't necessarily "the wishes" of those constituents.
Remember that an MP's constituents include everybody living inside the constituency, and not just the people that voted for them (or even just those eligible to vote). It's everybody.
Well they aren't random, but yes, pretty much. Anybody can claim anything on the campaign trail and then not follow through on it (*ahem Leave on the 31st October*), the whole point of democracy is that you can hold people up to scrutiny and then use the process to elect someone else in their stead once they are a known liar.
Now you're just being facetious. But I do think strong political parties are part of the problem.
That is literally how it works. I'm not defending it as a great system but that's literally what we have. This is of course not true of the referendum, where the liars have won and we have no democratic recourse to fix it later.