Hola. 1 is right, 2 is close, 3 is not the way it's used. 2. I picked up cooking by watching my grandma. (The object of the verb "picked up" needs to be a noun.) 3. Here you'd say, "I'm learning to be more patient." Pick up in this sense is just used for areas of knowledge not personal characteristics or other things.

1. Correct. 2. I picked up [ how to cook / cooking ] by watching [ my grandma / at my grandma's ]. 3. I'm picking up how to be more patient.

Oh, I should have put this in the comment section, because Ed has already done a great job with the answer. Your question made me think of another use of "pick up" Is Fred really interested in Spanish? No, he's just carrying on with the lessons so that he can try to pick up Spanish girls in the bar when he goes on holiday to Malaga this summer. Hmmm. They'll figure him out! His pickup lines are bad enough in English. Dave