From what you've told us in your OP, I wouldn't assume he's seeing anyone else, but unless you ask, you won't know.
You seem very clear about exactly what you're looking for in a relationship, so why not talk to him about what's going on in yours, so that you know exactly where you stand and if it's not where you want to be, you can move on.
I'm relatively optimistic and think that as long as you approach talking about the relationship with him in a positive way ("I'm really enjoying spending time with you and we have a great time together...") then asking where you stand shouldn't feel like you're pressuring him, simply that you feel that exclusivity is the next stage in the relationship.
In terms of spending so much time at your place, I would set up a trip out once a week; (on an evening when he has confirmed he'll be spending time with you) dinner, the cinema etc. and either make a reservation or buy tickets, then you can present it to him as "You mentioned you wanted to see this film/try this restaurant, so I've made us reservations for this evening!" I imagine spending the other couple of evenings you're together at home won't feel such a "waste" in this case.
You mention he hasn't introduced you to his friends or family - has he met any of yours? If not, you could arrange an evening in the pub (or dinner at yours etc.), invite a couple of your mates and ask him to invite some of his. I wouldn't stress over not having met his family at this stage though, that will come in time.
It seems you just need to sit down and have an open and honest chat with him, it doesn't need to be too heavy and if it turns out he doesn't see things going the same way you do, then you have the option to bow out now, before you get too invested. Fingers crossed though, he'll feel the same way you do, will be pleased to be exclusive and will agree that you don't want to get too 'settled' too young and he's up for getting out and about and doing things together.
Good luck, let us know how things go!