More good pics would be welcome, Including her tail - she may be medium / longhair...
She seems to be a spotted brown tabby. Possibly broken mackerel, but I think she may be spotted for real.
What a breed look alike? Its too early to guess.
If she hasnt no solid background story, we must presume the breed as such is domestic. As the great majority of all cats are.
Why she doesnt no longer sleeps with you - its impossible to know with this short info; but its individual. One of my cats often sleeps with me. The other he had periods when he slept with me at least some. But nowadays he perhaps lays himself on a chair nearby me... If missus is home they usually slept nights with her.
Welcome to TCS! StefanZ
gave you some expert advice. Regarding why your cat does not sleep with you it would be best to post a new thread in Cat Behavior so that it will get more attention here: Cat Behavior
BTW, your little tabby girl is adorable. What's her name?