A) Train him to not whine every time he's left alone (he's tiny and our Pits are not so we can't let him roam yet),
You don't train him not to whine. He already knows how not to whine. He is a little puppy. Puppies in the wild are never alone. Being alone is scarey to him particularly now because he is away from Mama and his siblings for the first time in his life. The less you leave him alone the better he will be. I would even put his crate in the bedroom at night and let him sleep in the room with you for a few months.
B) Introduce him to our Pits so that they won't see him as a chew toy? I had him on the couch with me last night with my husband right there. The Pits were curious but avoided Duckie. Thanks!!!
Assuming your pits are normal domesticated domesticated dogs, there is little you special you should do. Yes, they are going to be curious and sniff the new puppy a lot. They will probably be what you would consider rough with him but they won't hurt him.
Adult dogs are very tolerant of puppies and will let them get away with stuff he won't get away with when he is an adult. They will allow him to bite their snouts, ears, paws, tails, etc without getting angry with him. I say just put him on the floor and let them play. They will all have a great time.
When I brought my Thor home he was 12 weeks old and about 25lbs. Abby was a few years old and 135lbs. When we drove up, I let Abby out of the house and put Thor on the ground just outside the car and let them introduce themselves. They were great ever since. Never a problem between them. Yes, sometimes Abbywas rough with him but almost always he tried to get her to play with him so he knew what was coming.

He loved playing with her.
When we would go for walks Thor would get Abby to chase him. He knew she could catch him and he knew she was going to knock him down and bite him all over but he always tried to get her to chase him.
As he got older he could outrun her so he would slow down so she could catch him and beat him up again. Since she has gotten older, she will rarely chase him anymore and I can tell he misses it.
Anyway, I got to rambling ... sorry.

Don't worry about your pup and the dogs. They will do fine. The less you intefere with them the better they will be.