New puppy mom, not sure if I’m doing it right

This is Theodore! I adopted him two weeks ago from a local rescue in Phoenix and he is almost 12 weeks. He is very small so I am home with him almost 100% of the time or I take him with me where I go for short periods. He will eliminate outside, but he doesn’t have all his shots yet so we have another two weeks or so until he can be outside on grass or in dog parks, etc.. He has been pretty good about going on the wee wee pads in the house, but we do not have a set schedule. He basically eliminate when he needs to. I purchased a playpen that I can customize size wise. The issue is I noticed that he doesn’t mind being in the playpen, but once I close the door and he realizes he can’t get out he will cry and it’s very loud. I live in an apartment lol I’m also worried that I shouldn’t let him cry it out and I also worry about even leaving the house for more than 20 minutes these days I’m worried that I am not going to be able to prevent him from eliminating in the apartment on the wee wee pads even after his shots are complete. I also noticed yesterday I let him into my bedroom for the first time and it’s fully carpeted and he peed on the carpet more than once, even though he has never really peed outside of the wee wee pads. I guess I’m just confused if anybody has a really good straightforward piece of literature that I can read or any pointers on a 2-3 month old, I’d really appreciate it! He’s a very silly boy and very sweet. I just wanna do the right thing and not have issues with him. Going forward potty wise. I’m also thinking of putting him in puppy daycare to socialize and learn skills one or two times a week for a couple of hours.