1. If I am happy with my team and situation I would stay on the team and go down to AAA. I would be a little peeved if I was an established veteran, but just use it as a brief rehab kind of thing to get myself back into the swing of things and expect to be back in the big leagues soon.
2. I wouldn't get traded if I liked the team I was with and my team liked me. I could see if things weren't going well, but I would never waive a no trade clause if it wasn't obvious the team would become better without me.
3. I don't think anyone would just accept getting a paycut if they had the option of not taking it, but if its either take the cut or get fired, then I would take the cut since my play has apparently been sucking lately.
4. Hell no I'm not playing for the Yankees if they offer me A-Rod money, it doesn't matter, talk about embarrassing, being seen in pinstripes wouldn't be worth it.
5. Who they hell would be offering you a side offer, one if its a different team and you are signed already that is illegal, and if it was some other situation then that doesn't make sense, but theoretically, I would stay with my team since if you are a professional athlete you are going to be making plenty of money to live comfortably and being in a place with your friends is a plus. Why would you take money you don't need and be miserable.