No. You can cook a chicken but not rotisserie it.

Yes, it will do a good job. If you have a non-stick grill or use the included one, use 2/3 of the time your package instructions recommend.
Practically no allowance for warmup is required, though if it's still hot you might cut the time some.
The oven is large, 8" inside and more across; theck the catalog for size information before you try to squeeze it into a small counter. And leave some room around it, as well.

Too large a question; what size, type and shape are the potatoes in question.
Basically, count on getting the cooking done in 2/3 the time for most foods, but the nearer they are to spherical the less advantage you'll have.
If you're using medium-size russets, you're still looking at 60 minutes or so at 325 degrees.
Microwave is much faster (check your instructions) but it's not really the same thing, is it?

Yes it does have a rotisserie on it. This oven is great! You would love it.

I wouldn't. It is bigger and heavier than most microwaves.

The top oven picture shows 2 elements each, top and bottom. If only top elements, oven would only broil, toast on top and not bake.

The jury is still out on 9"x13" pan fit.

It has a few recipes in the instruction manual.

Pretty easy, except for the very, very top. The bottom comes out like a tray, which is great. I love it!