They were mating again today

The male keeps going into the nest box, making this weird crying noise and then he will come out. It seems like he is trying to lure the female to the box or something. I don't know exactly how to explain the noise he makes but he only does it when he's in the box and it usually entices Rasta to go check it out. She has only been about half way into the box so far but it's only been about a week so I'm not stressin' it.
I have never seen birds mate the way these guys do either, Reggie doesn't actually climb on her back at all, both times it has happened, they have been on top of the cage and they just kind of sit right next to each other and he puts his tail under hers and they do their thing

Is this normal amazon mating? She also puts her head down and holds the bar on top of their cage with her beak. Sorry for such a weird question lol.
I also have been giving them free access to be in or out of the cage since the third day they have been here. Originally, I let them out during the day and then at night I would just put some treats in their bowl and dim the light and they would both go in so I could close the door for the night. After the first two nights they got wise to this and now they've devised an evil plan...One of them always sits on top of the cage. They take turns going in to eat and no matter what I try I can't ever get both of them in the cage

At first I was kind of upset that they were doing this but then I realized that's it's always been sort of an unspoken rule that if you don't leave your cage then you don't need to be locked in. That's what we do with ziggy, I don't think her cage door has been closed for a couple months, she is almost always out, unless she is eating or sleeping or wrestling with her toys but she NEVER leaves the cage. So for now, I've been leaving their door open as well, although if I have to actually leave the house I'll be sure to get them in, I don't quite trust them enough yet to be left out unsupervised. But back to the point I was getting at, is there anything wrong with allowing them out all the time when we are trying to breed them? I would hate to have to lock them up, I don't know how long they lived with their previous owner but he didn't let them out of their cage, ever. They seem so happy now that they can be out and on top, I don't want to take that away from them.
Oh, one more thing, I caught one of my female budgies in her nest box today as well! She's had the box since early december and hasn't shown much interest in it until now, so hopefully we will have some budgie babies too

Sorry if my writing isn't very comprehensible today, I've been feeling horrible(sick) all day and I think it's affecting my brain:52: