You can easily tell if an ipad is using wifi or not. Just look at the icon at the top of the ipad. If there's a wifi symbol then you are on wifi. If there's a 3G, E or a dot then you are using mobile broadband.
As for screen protectors, personally I think it's a must. Even for screens with gorilla glass, I'd personally rather have one than not. My logic is that it's better to have one than none.
You can get a pack from ebay for really cheap. If you've never done it before, I recommend getting a few as it's a bit fiddly.
My tips are to use a glass cloth and screen cleaner to polish the screen. Shine a lamp onto the ipad and using the cloth, make sure there's absolutely no specs of dust at all. This can take AGES! lol
Also have a roll of good quality sellotape to hand.
Peel the first part of the screen protector off slightly, align it the best you can and start peeling it back, using a small piece of cardboard or credit card to smooth it down slowly.
Once it's on, use your glass cloth to get all the bubbles out. This is where you will find out if you've got dust still on the screen.
If you have, use a piece of the sellotape to lift the protector off, do NOT use your fingernails. Use another piece of sellotape to dab the dust particle off and then reapply.
Patience is the key and with luck your protector will look completely invisible.