The instructions say not to use it that way. Probably because of the teflon coated aluminum grill...would have been better if it were made of cast iron in my opinion.

Yes they do.

I have not measured it but the cooking service is as big as an 8 1/2 by 11 piece of paper. I cooked pancakes and bacon at one time on the griddle. I cooked 4 good sized steaks on it at once.

Not sure what kind of cover you are asking about. The stove comes with a griddle. To use it you just take off the grill grate and put the griddle in its place. When you are done with the griddle, you put the grill grate back in place. They just exchange out. There is no cover that goes over the griddle.

Yes it does and it is all teflon coated for easy cleaning

Yes, tabletop grills can be used with larger tanks.
http://www.walmart.com/catalog/product.do?product_id=8587357

I believe that this is also sold in most stores, too.

No. That has to be purchased separately.