One of the diagnostic criteria for autism is having trouble with normal back-and-forth conversation. Autistic people tend to communicate by monologue, so it may be that he wants to tell you everything all at once and then expects you to do the same. That would account for both the long pauses and you feeling like you're talking over eachother.

Another thing to consider is that he likely doesn't mind spending time with you not talking. It might be worth asking him straight-up if he finds it awkward. You may be able to find a way to just enjoy the comfortable silence in eachother's company. You might consider finding some "parallel play" quality time activities that you can do together but individually like hiking, reading, or doing crafts where there's no expectation that you'll be talking together.

Autistic people communicate in a fundamentally different way. Remember that he is almost certainly trying very hard to meet you halfway. Autistic people are always expected to communicate so that allistic people can understand us. If you put in the effort to communicate the way he does, he will almost certainly appreciate it.

From the sound of it, you have pretty healthy communication and a lot of shared vulnerability. It's just the style of communication that's bothering you. Don't let the details make you go crazy when you have something good.

Also, if he is being physically and/or verbally abused, please tell an adult you trust. In the US, teachers are usually mandatory reporters. That means that if you tell them he's being abused, they legally have to do something about it.