Does Asterion actually romantically love MC? 

What the title says... Would Asterion actually love MC, seeing as he is hundreds of not a few thousand years old. Would he see MC as little more than a child (emotionally/mentally, not physically)? Would it be possible for him to even develop feelings for someone so many years his junior?

I'm not being theoretical, I would really appreciate everyone's thoughts on this. :)

The short answer is yes. Past the legal age, intergenerational affairs only depends on if all parties are interested. Although there are good reasons someone who lived as long as Asterion wouldn't want a relationship, the story is very clear that MC and Asterion can end up together. In fact, Asterion is the only one who MC will be able to end up with according to the devs.

I like this question! I think it's clear that Asterion has feelings for MC, but I find it difficult to answer the question "could an immortal being form a meaningful relationship with a human who will inevitably pass away?" in general. As you mentioned, it might be difficult to see someone on the same level as you intellectually if you've lived hundreds as many times longer than them. I also wonder how much it would wear on someone to see their loved ones grow old and pass away over and over. Would that make it more painful to form connections, and would they wind up avoiding such connections to avoid the hurt?

I don't see either of these being a problem for Asterion, however. He has plenty to learn about modern society from MC, and plenty to share from his own experiences, which lets them see each other as equals. He has also had few former masters that have treated him well, so he hasn't become hardened by losing generations upon generations of loved ones. He clearly wants to get to know MC and isn't apathetic to the attention given to him.

As a last note, I just finished rereading Circe by Madeline Miller, and that book grapples heavily with the relationships between gods and humans; some gods are clearly hardened by their divinity and don't spare a second thought to humans, and some are intrigued by the imperfections that humans have. I really enjoyed it, and you might, too! (Not to mention that the legend of the Minotaur of Crete is a big event in the book :) I got a kick out of rereading that part after having played Minotaur Hotel!)

while it certainly helps that the MC is humanity at its best, I think for me the most interesting concept here is queer time. While Asterion has lived for ~3000 years he has spent almost all of this time seeing being treated and believing himself to be less than human, with absolutely no opportunity for a romantic relationship. When interrogated by Jean MC understands his relationship with Asterion well he is on the ball considerate and its clear he understands how to have a romantic relationship. Asterion on the other hand is just learning to admit that he does have feelings for the MC the blunt "he wants" being the description of how he feels in a game that does not shy away from long metaphorical descriptions is the same as that used to describe how Khenbish feels near the end of his growth which is literally a story about coming out. so we help Asterion come out from the closet a little bit and he is now following the ideas of queer time he is like a child everything is new to him, and so there relationship progresses at his pace where he is the young one and so their relationship forms the pattern of young love with stupid nicknames and blushing while holding hands at the movies. MC is ready to F*ck at chapter 15, the first kiss doesn't happen until chapter 18.