I'll go loosely by the bullet points to make this wall of text have at least some structure.
1. I'd like to see a bit of role reversal where the MC can take or (if Asterion is sufficiently riled up) yield the more active role in a scene, or (smoothly) push Asterion into the bed/pillows to end up on top of him. In terms of kinks, bondage and latex (clothing or accessories) are personal favourites (though I don't know how well the latter would work with fur, considering the game seems to otherwise take a realistic approach). Being able to masturbate/top and/or interactively edge him manually and/or using toys, similarly to the kiss scene, would be really hot.
I love the occasional surprises about how Asterion's body works. I suppose that's less of an idea and more of a "more of that please", though.
2. M3tav0X's idea of riling up Asterion with hypotheticals is verz hot. More casually, the MC unexpectedly revealing that he's (very) open to trying some thing or other and getting him flustered that way sounds very fun. (On my main playthrough, it's unclear how much experience the MC actually has, but he's not shy about drinking games.)
3. I have the strong suspicion that, if the topic comes up, Asterion could use internet research and contracts to make sex toys, especially interactive ones. (From what I can tell, he could easily do this on his own by skipping the electronics.) He could probably even tweak them on the fly if needed, though handing a stealthy "linked object" remote to a more sexually dominant MC seems fun too.
Also, as others have mentioned, he seems like he might slip the MC an invitation or other message in form of a poem sometimes.
4. There's a contract somewhere that makes Asterion feel the Master's pain, right? (I'm not sure he ever mentions this out loud, though.)
It may be possible to amend that one to a) temporarily replicate other sensations like touch and b) also work in the other direction.
(Kinky idea: Maybe this could even be used to act as temporary body swap that works between the MC and Asterion specifically. That would make a really interesting late NSFW scene.)
5. Bondage is a touchy subject in this situation. I think Asterion may be okay with it or even into it if it's light and doesn't involve any hotel or labyrinth magic to restrain him (beyond summoning physical but otherwise mundane restraints, likely ones he could break out of with some effort). He may have some unusual preferences related to how his body works, that would be interesting. There may also be a need for an additional contract that limits the Master to make the scene safe for Asterion.
(I'd actually like it if the MC could state very early on/in advance and unprompted that anything involving pain is off-limits, in both directions, due to the proximity to BDSM. The labyrinth seems to enforce one of them anyway, but this is a different context not built on contracts, so I think it bears restating.)
Manipulating Asterion's body would be interesting as Theodwulf mentioned, but I don't think he'd be okay at all with his mental state being changed directly this way (and it may not be a good idea to do this even if he requests it for some reason). However, he may be able to become much more comfortable with this part of the situation if the MC uses this to pleasure him more indirectly by adjusting shapes and/or sensations (but in either case, I wouldn't be comfortable with doing this without confirming consent and boundaries first).
6.&7. To be honest, I have no idea where I even ended up on that scale. Determined Asterion is hot as hell and he's utterly cute when flustered. I want to directly compliment him at some point, even if it's a bit blunt. Topping him while he's not entirely submissive would be great, I think. And cuddling afterwards.
8. It's hard to tell. I think he may be into kinks that let him safely explore parts of his past trauma, but outside of that I suspect he'd also want MC to have a more hands-on approach to his culture from when he was alive in Crete. Or to himself in such a context, for that matter. Maybe he'd prepare a set of clothes for the MC to wear going into such a scene, especially if he recreates the climate from Crete there and it doesn't match the hotel's.
(final edit: Just went over this again, hopefully it's a bit more coherent now.)