I just kind of went through #2. And the best answer here seams to be go with, and I am choosing a Weber Q series. I went with the 220.
If you mean like camp stove I recommend a Camp Chef. About the only thing I cook inside my trailer is boiling water, and baking in the oven. I do all other cooking outside as to ot mess up the inside. I set everything up under a 10x10 awning. If you are a coffee drinker you have a few options, I shoose to go witha french press as it is easy and does not require any electricity.
#6 look at walmart, or even if you are upgrading to new stuff int he main house move the old out to the TT if it is good.
We have kids so we use a lot of plastic ware and paper plates. Easy to dispose of fairley water wise if you are boondocking, nothing to brake. I still have some plastic cups and plates for things like steaks but they hardly get used.