I have a 4.5 year old and a 2 year old boy. My eldest is very similar. Being the first is different than any other child. Even though you didn't "spoil" him he had all of your attention for a while when he was younger. He's used to of having someone be there for him. It was his "norm". Then came 2nd baby and things changed for him. And now he's headed for yet another baby coming. I really would suggest spending some special time with him. You don't have to go anywhere or anything like that. Just try and get on his level a little bit every day and let him take the lead with you in it. Play, talk or hang out and watch a movie. It will do wonders for you both! You know, connect with him again. As for him wanting to do things for himself, let him. And be encouraging of it when he does a good job. I know for me, I have a really hard time realizing how much my son can do until I see just how well he does them.As for the fit throwing, well they are a part of him trying to learn self control. He gets frustrated just like the rest of us and hasn't gained the skills to deal with them yet. Try and not give him attention while he's doing them and try and validate his feelings after he's calmed down. Talk about what happened and what he could have done different. If he's throwing a fit in public be prepared to drop everything and leave, after a few times he'll get the idea. It's tough to do but if you know you might have to leave you'll know ahead of time.
Sometimes we can just get "put out" with our children and they know it. For us it's overwhelming and frustrating, for them it can be scary and unsure and they can act it out in their behavior. I can imagine that it must be a bit overwhelming for you now with another baby coming so soon in your future too. Congrats on your new family member!
I started homeschooling Kindergarten this year with my eldest son! We love it. We are almost done with this year and can't wait for 1st grade next year! Happy Homeschooling!