My 11 week old pup pooped in the crate 4 times last night. What can I do?

Please help!! I purchased an 8 week old Yorkshire Terrier and kept him for 3 weeks without crate training. After too many "accidents," I've decided to use the crate (I had tried it several times during the 3 weeks, but could not stand the constant whining and barking), I hope I'm not too late. I'm dedicated to seeing this through this time, he's 11 weeks now. I have some very specific questions. Last night, I took his water up around 6 pm and took him out to pee at 8 pm and 9 pm to crap (he craps about an hour after he pees). Well, he barked and whined the entire night. My question is, since he barks all night, when I go to let him out in the middle of the night to pee, is that teaching him that his barking works? Should I not go to him at all while he's barking? Every time that I did get up to open the crate (which was about 4 times), he had already peed or crapped in the crate, is there a specific time limit for puppies this young? Also, when that happens, should I just clean the crate and put him back in or should I let him run around a bit, even though he's already relieved himself? Since he craps so much longer after he pees, should I wait and let him run around for an hour or should I put him back in the crate, then come back an hour later to crap? Also, I put my arm out to pet him yesterday, and he started "humping" my arm. Obviously, he's a male dog. Is this normal? How can I curb this behavior?

I really appreciate your help in these manners. Hopefully, day 2 with the crate training will go smoother!

Sincerely,
Charifa