First off, it might help to have a reference picture of the character in question. Not everyone is familiar with Team Fortress. It would also help if it was a picture of the specific version you want? The one you have is just the body, not the mask or gloves.
1) Try looking for a catsuit/bodysuit pattern and altering it to your needs.
2) Are you talking about Vinyl? Yes, that fabric doesn't breathe very well, although it is shiny like the Pyro. Maybe sacrifice a bit of accuracy for comfort? How about Spandex/Lycra? Not sure how much it costs though.
3) This mask looks quite a bit like the Pyro's, but you would have to somehow add the side cylinder. maybe use a can of some sort and paint it? http://www.goldnuggetsurplus.com/mm5...uct_Code=CE002
4) What kind of gloves are you using? Rubber gloves? Not sure what you'd use to paint those- Try looking up how to paint latex, rubber or vinyl, depending on what they're made of. You'd need some kind of flexible paint, maybe paint mixed with latex or something of the sort. I know fabric paint is somewhat flexible, but I've never painted rubber, so I'm not sure it would work...
Are you painting it in thin layers or in one big thick layer of paint? I've been told it's better to paint in thinner layers.