I think that 'affection' is a better word here. If your cat shows affection, it means that he or she knows you, likes you, and enjoys cuddling up to you and purring.

I think Su.Ki is right, 'affection' would probably be more appropriate here. As for the difference between the two, "love" tends to be used with feelings, whereas "affection" tends to be used with actions. This isn't always the case, but in general that's how you can think of it. "Affection" tends to be preceded by "show" as a result of this, e.g. "My cat showed me affection after I have it food."

Question 1- Love- To really really like. Affection- To show a liking towards. I really really like him. / I love him. You show a liking towards him. / You show affection towards him. Question 2- "My cat shows affection (towards me)" [with or without ")("] or "My cat show love (towards me) [ < sounds a little strong] :P