1. I have these type days and typically it means I'm starting to venture into overtraining territory usually because I had a few hard days at work. I typically notice it when my nose is stuffed up in the morning, bad nights sleep, and elevated bp and pulse. I take the day off in those situations, get a 6 pack of beer and soak in the hot tub.
If I don't have signs of overtraining I will do my normal workout with what i feel good with. You are not going to be increasing strength or at max strength all the time and some days are just off worse than others. Those days are just a mystery so train through them.
2. Assistance for me are just that, and secondary. I concentrate on my main lifts and assistance goes how it goes. If I can add 10 lbs to my deadlift I dont care if it blows up my assistance for the day.
3. I don't like extending rests beyond 2-4 minutes since I want to be done in an hour or less. I strip plates off if thats what it takes to get done. I lose focus after an hour.
disclaimer: I'm a noob at powerlifting