Actually cats are very sensitive to emotions, especially towards the human that the cat had decided to be his/her "leader" of the pack (known as owner, cat do not acknowledge us as their "owner", rather they see us as their "leader"). My cat took me as her "leader of the pack" and will follow me around the house when she's not sleeping. With the normal cats' instinct built-in, she does sometimes do things that "hurt" us, like example what you had mentioned : "nails/claws out while playing with us".
Cats can be trained, and depend how you going to "communicate" with your cat. For me, I treats my cat like a kid, which needs to be taught on things that are correct or wrong. Which means I teach her like how we teach a human baby, like example while a baby is drinking milk, we repeatedly tell them "milk milk", or while defecating we repeatedly tell them you "poo poo". Babies and cats/dogs can learn simple sound (repeated sound) and able to associate the sound with the thing they are doing at the moment after several times of repetition.
Example what my cat had learnt:
- When she play with us and unintentionally pull out her claws, "Ouch!" does not always helps as she don't understand. I repeat the word "pain pain", whenever she dug her claws on me, after a while she understood that "pain pain" means she's hurting me; and automatically she'll pull back her claws.
- While seeing her jumping onto a chair or table, I'll repeat the word "jump jump"
The next time I saw her below a chair or table, I say the magic word again, she will understand and followed my "instructions".
- I made her do some trick to get her favorite treat, I'll say "hand hand"; which means I want her to raise her paws for me to get the treat. It does work! (but only for her FAV treats, Haha).
Different breed of cats does have different level of intelligence which I watch from "Cats 101" though. You may wish to try it out for a few times, and hopes that your cat could finally understand and able to "communication" with you.