Won't they like sucking the lycra?

Not likely, it has a different feeling than the bare thumb which has a comfort element hence the perennial habit.

Does it come with just the one guard?

Yes. But seriously, don't waste your money, it honestly doesn't work with any kid who is just half-clever and wants to suck their thumb. They can take it off, or even (!) suck the thump with it on! The Mavala stuff you brush on like nail polish on their thumbnail is like magic. It may sound "mean" to some, but I did it with my 4 yr old son, and he stopped cold in like 2 days (and only 1 or 2 mistakes where he forgot). I put it on my own fingernails in solidarity (I used to bite my nails), and stopped that habit at the same time! I also gave him some tic tacs to keep with him overnight in case he forgot. Worked like a charm.

my baby girl is 3 years is this product matches her finger or for kids not babies ??

not really for babies but it is stretchy, so you could possibly make it work. But it really helped my son and it washes well. We also bought a different one on ebay. It was a terrible product for more money this one was way better.

Does this fit a 3 year old or is it for older kids?

Yes, this would fit a 3 year old. As I have reviewed, there is an inconsistency in size of the wrist strap. The last one that we purchased, would fit your child perfectly!