There's a lot to unpack here, OP. The biggest thing you will need to tackle is betraying his trust and went through his phone. That's not going to be a fun conversation for either of you. However, it's something that is going to need to be done if you want to continue in this relationship. And the longer you wait to bring it up the worse it's going to be.

It's a shame he didn't feel comfortable enough to open up to you but sexual preferences can be a touchy subject for people, especially depending on what the preferences are and what their upbringing is.

Now as to what you found, I would not be too concerned based on only what you saw. Just because he likes x doesn't mean he doesn't like y and z, too. I'm other words, what he searches for has no bearing on whether or not he's attracted to you. That's something you two will also need to discuss. There's no reason at this point to indicate that he does not find you to be beautiful, sexy, and attractive so please try to stay calm and keep an open mind when you talk to him. Getting upset will only make him want to close himself off.

Finally, the search term 'teen' doesn't necessarily mean you're too old for him, either. It may be simply that the teens of that group have a more feminine appearance for him.

I typed a lot, but what I'm trying to say is you need to talk to him and if you love him you need to be accepting of whatever he says to you.

Finally, though, if you two are living together and sharing expenses while barely making your bills and he's hiding subscribing to web sites that is not okay. He shouldn't be doing that and breaking your budget while you two are trying to build a future together.