Don't worry, my 17-month-old is exactly the same with our three (yes, THREE) cats and one puppy. I'm convinced she's trying to kiss them because she always kisses with her mouth wide open and tongue hanging out, and she makes the same 'mwa!' noise when she does it to the cats as she does to us.

As long as the cat is wormed and flea-treated, you shouldn't have any problems, although it would depend again on whether kitty is an inside/outside kitty or strictly an indoors cat.

As to the rough play, just keep an eye on it. Two of our cats are AMAZINGLY placid, DD can drag them around and 'cuddle' them (really roughly, poor things) and they will sit there and take it, and have never shown any aggression or ill-will towards her, but the other one (because he's an older cat, and was a sole pet until my husband's mum died and we 'inherited' him) isn't quite as happy about having his ears pulled or being sat on. So we just tell DD 'no' when she gets rough with them and she gets the hint once she's had a giggle at cuddling them once or twice and finds something else to amuse herself with.
Our puppy isn't aggressive at all, just playful, and nips her when she is in a vulnerable position (laying on the floor or crawling), and sometimes she cries but mostly she just laughs and roughs the puppy up as much as the puppy roughs her up. We're trying our best to discourage this though as we know dogs need to know their place in the pecking order, so she's getting much better with puppy class and we're confident things will be fine with them.

Good luck with yours, I think it's great that you are bringing up your bub with a cuddly pet to play with - it teaches them so much about life, love and caring for another creature that we can't teach them ourselves. They will be best mates as they get older and your bub grows out of the rough stage, it's amazing to see how they interact with each other.