1) I've seen that in a recent game as well. I declared war on someone who was Close, and a couple turns at war and relations were still Close. Relations take a few turns to deteriorate, depending on the +/- difference. In that case, I had same ideology and high diplomacy skill and few other minuses.
2) That's one of the major flaws with Diplomacy at the moment. The scale is far too narrow, allowing for easy diplomacy exploits or overwhelming Ai aggression to happen far too quickly and easily. Players are forced to invest heavily in diplomacy to counter, or build a huge fleet to fight off the aggressors. There should be some middle ground.
3) Maybe your power increased to a point where they thought they should bribe you rather than menace you 
. I get minor races threatening me in games...it's just flavour most of the time, nothing ever comes of it. If the Ai doing it can reach you and has much more power than you, then sometimes it's a warning that they're going to declare war soon.
4) Currently it's more of a sliding scale, where things get better or worse over time. I believe it is that way so players have a chance to change the course of those events should they choose to. As you pointed out, there isn't much time to do that right now, which kind of ruins the system. In most cases the sliding scale makes sense - you don't want to go from Neutral to Hostile in 1 turn because you did/did not do something to keep the +/- balance. Remember as well that stuff the Ai does affects the balance as well.
But you're right, in some cases it makes no sense, like the example I mentioned in #1. Going to war shouldn't just give a -3, relations should go straight to furious.
I agree with you that SD should do a lot of work on improving diplomacy - it affects every player in every game in some way. I guess we'll have to wait and see
