Mini Dachshund with a huge attitude

Hello!

We have had our mini dachshund for around 2 weeks now. He's 12 weeks old. He's supposed to get his last vaccine tomorrow, so he's staying inside. We've done a road trip to my parents' apartment and things went pretty well.

The little dude gets very quiet when he meets new people. The first 2 days he barely moved and we thought there was something wrong with him. He was just frozen. It was the same when he met my parents – he would keep super quiet and just sniff around.

Things completely change when he's alone with us. He keeps stealing socks, running around, and most importantly, biting. We keep telling him "No!" but I don't really know if he understands that word. He will grab my finger and I will keep saying "No!" to no avail. Whenever he understands that we are upset with him, he will bark back and continue biting. We used to cuddle on the couch together but we don't really let him up here with us anymore since he gets too excited and starts biting. Whenever this happens, we always say "No" and put him in his bed and remove the ramp, but I don't know if he understands that biting is why this happens.

He has plenty of toys and he knows that they're great for biting, but he still loves stealing shoes and slippers. No amount of saying "No!" seems to persuade him not to do so. Also, he'll prioritise fingers over toys quite often.

We've managed to potty train him to pee and poop on a potty training pad and he's pretty good at it until he's not. When we're not looking at him, he'll pee where he's supposed to. Sometimes he pees on the edge of the mat, but that's acceptable. Sometimes, though, only when we're around, he'll pee in the middle of the room, looking at us. I genuinely think it's got something to do with us. We keep giving him treats when he pees where he's supposed to, but random "accidents" keep happening.

I understand that this is a difficult time and I'm proud of the progress we've made but I feel like he thinks he's the boss and he can bite whoever he wants without repercussions. How do I set boundaries for when playtime starts and ends with a puppy this young? Thank you.