G.♣.
Your son is telling you that he needs you. He may not realize this himself, so he may not be able to articulate it. He is telling you that he is insecure about this new guy and is afraid that the boyfriend will be more important to you.
Think about what you can do to reassure him. Consider what the bedtime routine look like now and how you might be able to tweak it in ways that he likes. What can you do to make it more special to him? if you don't already, maybe you could read a book to him or read a book together. It's not uncommon for kids to want to come into their parent(s)'s room at night - especially if they are feeling insecure about something. While you don't want to start letting him sleep in your bed, try not to be too upset with him about that one. Stay calm and just remind him that you need your space (just like he does). Definitely do not allow him to think that you wanting your bed to be your private space at night have anything to do with the boyfriend (don't know if the boyfriend has spent the night, but when you talk to your son about it, make sure this is just about you having your own space and not about the boyfriend).
I would give in on the not being alone with the boyfriend in a room and not hugging/kissing in front of your son. Not that there's anything wrong with these things, but give your son some time. If you back-off on those things and give him some time to get used to the relationship and get used to the boyfriend and begin to trust you that his (your son's) place in your world is not going to change, he'll get past it.
What your son needs is lots of reassurance from you and time.