After removing old paint from a concrete patio, can I just stain? Or should I do more to improve the outcome of the looks & last of the new stain, also can I use stain with multiple colors to achieve to look of rock at the same time?

after removing old paint from a concrete patio, can I just stain?

Almost


or should I do more to improve the outcome of the looks & last of the new stain,

That depends on the manfu specs of what you are going to choose.


also can I use stain with multiple colors to achieve to look of rock at the same time?

Again depends on how they stain is applied and what your skill level is

I attached some vids to give you some ideas and what's involved here. The vids will impress you on the 100s of ways to satin Crete/treat Crete.

YouTube - Soycrete Concrete Staining Indoor and Outdoor Projects (http://www.youtube.com/watch?v=BdlPSKGRG4U)
YouTube - Acid Stained Concrete (http://www.youtube.com/watch?v=CUhZEQ9c7bc&feature=related)
http://www.youtube.com/watch?v=DvL9NWPPRXY&feature=related