Assuming you mean electric radiant and not hydronic radiant...
1) Depends on exactly what you're doing. What type/size of tile? Any floor height restrictions? What's your subfloor construction? How much square footage are we talking?
2) You certainly don't NEED to do the entire area, but keep in mind that the heat will only be in the exact areas you have the wires/mats. It's not going to spread over your whole floor. I would strongly suggest you do the entire floor.
3) You mean besides
www.suntouch.com?
Nuheat
Flextherm
Warmup
Nexans
There are one hundred and one companies doing this now, and most are pretty much the same, quite honestly. I would say just make sure you get one that has a dual-conductor wire, and compare the warranties and materials used.