No this is not normal behavior for a 12 week old puppy. It is recommended that Yorkies stay with their mother and litter mates until at least 12 weeks of ago. You brought Oliver home at least three weeks early which could be causing the issues that you are experiencing. You really need to get these issues under control or things will continue to escalate
Having a trainer is a great start and as Gemy suggested you should speak to your trainer about the specific issues that Oliver is displaying.
He's not too young to start training to work for his food. Some of the things that you are saying might suggest that he might begin to display guiding which is very hard to break. Be sure you can handle his food while he's eating and that he will give up toys without guiding them.
I'm speaking from my own experience with one of mine~Pebbles. She is a rehome and came to me at 5 months old. Little did I know she was already guiding her food and had bit the former owner over her food. She left her mom way too early and to this day has many issues that we are still trying to correct at 5 years old