I would say all that is normal. Some cats like having their tummys rubbed, some don't. Sounds like your cat is one of those who don't like it. My kitten likes her tummy rubbed sometimes, but other times it is "attack!"


Same with the picking up - one of my cats (Abby) hates to be picked up - but she will come up and snuggle, jump in my lap - but only when she wants it.