His priority should be the relationship with his DC so that is reassuring that he's aware of that.
Of course having more children together would be nice, but at 5 months in this isn't exactly a given, definitely worth discussing of course to clarify you're on the same page, but absolutely not accelerating things in order for that to become possible. Wouldn't you think that was crazy if somebody didn't have children already? You don't know somebody well enough after 5 months to determine whether they would be a good fit to raise children with, that doesn't change because you already have DC, and there would already be a large enough age gap that there's really nothing to lose by giving that particular goal a few years. There is time enough in the future, and the priority needs to be the needs of the DC you each already have before you think about bringing more children into the family set up. It's unfortunate if this is unbalanced and his DC have higher needs than yours but that is something you'll need to accept - if you can't then it might be a question you need to ask yourself as to whether you can really take this on, as he does come as a package with them, that can't be avoided.
Yes it probably is valid to explain to your DD that you have a boyfriend, he shouldn't be hiding in closets - but really he shouldn't be in a scenario where he needs to hide in a closet! And there's a huge gap and scale from telling her that you've started seeing someone to her being happy with him spending a lot of time at your house - that needs to happen more slowly and I think it would be appropriate for her to learn about him from you, then meet him a few times on neutral ground (not at home) before she meets her at your house or he starts spending extended time there such as several-night visits, even if she's not aware of this. A night here or there when she's absent is more appropriate than him moving clothes in and staying over 3 nights of the week. I also find it a bit creepy that he gives you reports about her yet she has no idea who he is! Sorry. The September deadline is okay, I think, for them to be acquainted and have spent some time together before you go to the wedding but I would not be looking to move in together this year. That is far too soon IMO (and IME).
It is lovely to spend time together in a new relationship but I'd really be questioning whether it's not a bit fast to be spending so much time together just yet. What is the harm in taking things slowly and separating things a bit? You do each need time for yourselves as well. The other concern is that a partner being very full on, wanting to spend excessive time together, being overly enthusiastic for the next stage is a red flag for controlling behaviour. As is him claiming that his ex was emotionally abusive. Perhaps she was - but sometimes this can be a deflection tactic and it's just worth being aware of the possibility.
I am not saying that he is definitely controlling, as he might just be vulnerable/naive himself. I'm also not saying you should split up but I think it would be sensible for you to both dial things right down and be a bit more aware, especially in a small village, it's like a petri dish for drama and resentment. This whole we're going to be together for life after 5 months and needing to be in each others' pockets constantly is almost teenage in the way it comes across - sorry if that comes over as patronising, but I can't think of a nicer way to say it.