Here it means something more general: similar in political views, values, the way you talk, etc.
Quite. But I would propose "you are like your father" (or even "you are just like your father" (a typical saying by mothers)) as [a] good English rendering[s].
I agree with JerryMcCarthy99: "You are like your father" would be the natural English phrase. "similar to" sounds too formal to my ear.