What does my kitten mean when she does this?

So, I adopted a three month old kitten from the streets. We have a great relationship and all, she rarely bites now and sleeps with me at night either curled up at my neck or on my stomach purring, and kneads my arm all the time. But sometimes during the day when she wants to play with me, or whenever I'm sitting on the couch or the floor or in reachable distance, she likes to pounce on my hand or feet and try to bite or swat with her paws at it. Is she just playing, or is it something serious? Also, when we're playing a little longer, her tail starts to move from side to side. Is this a sign of aggression? And, can cats remember you by smell? Can they see colors? Remember homes? Thanks :)