My time has come! Words cannot describe how many ideas and scenarios I've come up with about Asterion!
Answering the prompts in order:
1) For positions, MC and Asterion in a mating press is very high on my list, as is Asterion riding MC cowgirl style. Sixty-nine with Asterion would also be pretty hot!
For sexual acts and/or kinks, body worship is an obvious one, as is role reversal. Some role playing would be nice to see, too. Pet play could also be something interesting to explore. It might be interesting to sometimes get an option to bring one (or more!) of the other characters into the action every now and then.
2) Tugging on and playing with Asterion's tail would definitely be a good way for MC to tease or rile Asterion up. Some of the banter between Asterion and MC could also lead to some interesting ideas; for example, MC could leave a pair of his underwear on Asterion's pillow if you choose the option in chapter 18 that suggests Asterion might do something "indecent" while doing MC's laundry.
3) I feel like Asterion would be really into more classic stuff for teasing and riling up MC; caressing, grinding, whispering sweet nothings into his ear, etc. Including new events where MC can show interest in various different kinks or ideas could be a good gateway into new ideas for Asterion to Tease MC with; for example, perhaps there could be an event after building the gym where MC can show an interest in body worship (sniffing, licking, groping, etc) in the locker room and afterwards, Asterion could "forget" to put on deodorant after a workout or "accidentally" leave a used jockstrap in MC's room. Really get creative with it!
4) The sauna idea is definitely a good one. Other ideas could be things like:
a. Upgrading the infirmary and MC and Asterion can decide to "christen" one of the new beds
b. Creating a playground with a swing-set for any children at the hotel - after an optional conversation with Luke - leading to the installation of a sex-swing in the Master's quarters
c. A rock-climbing room/station being added to the gym (the idea here is something like nude climbing)
d. MC getting the opportunity to view the contract that forbids Adsterion from "exposing himself while [they] are expecting guests" and having the opportunity to modify or even completely rescind it would be a neat idea to explore
e. A game/club room with things like a pool table (getting to tease or fuck Asterion while he's bent over to line up his shot; MC being teased or fucked by Asterion while bent over)
f. Similarly to the sauna, adding something like a public bath or a proper onsen as a surprise or at the request of Kota, and/or adding a hot tub/jacuzzi to the pool
g. Building a spa where MC and the characters can get massages and other spa treatments that can temporarily improve their stats, similarly to cooking with Khenbish
h. Instituting an "Adults-Only" time at the swimming pool where swimwear is optional, encouraged to be disregarded, or even completely banned
i. Maybe something like adding giant themed "getaway-rooms" that resemble different places and environments; one could be themed after Paris and have a perfectly to-scale recreation of the Notre Dame cathedral; another could be themed after the Asphodel Meadows in the Underworld, or perhaps Crete as Asterion remembers it
j. A dance/martial arts studio (open room, wall-length mirrors, etc)*
k. Art gallery (calling Asterion or his body a work of art)*
l. A big library (fooling around with Asterion in a secluded cornr, but having to stay quiet; filling it with books could be something achieved over time via donations from guests and making purchases through the R&D Projects menu)*
At the end of the day, it really comes down to how creative you can get with seemingly innocuous or innocent projects. Really stretch the limits of logic and creativity with it!
5) Bondage, maybe? I don't really have much of anything for this one. Ultimately, I'd like MC and Asterion to establish early on some sort of safeword or consent agreement where they can explore their more out-there ideas and urges, but only as far as the other is comfortable.
6) Dirty talk about what MC could make Asterion do, filling Asterion's head with ideas of all kinds of horny debauchery, only to say that Asterion will have to ask for it if he want's anything like that to happen. Playing with the dominance and power dynamic while ultimately leaving it up to Asterion to decide what he is or isn't comfortable with pursuing.
Additionally, while MC and Asterion are getting frisky, MC could grab Asterion by the horns and fool around with that; grinding into his muzzle, getting a touch more aggressive while receiving oral, etc.
7) In a situation where MC is just less dominant, I don't really see Asterion becoming more dominant on his own. Rather, I'd like to see paths where MC could actively encourage Asterion to be more dominant in a sexual setting; for example, using the hotel's magic to tie himself to the bed, ready for Asterion to use as he pleases for awhile.
Heck, maybe even have a more dominant Asterion pull a trick like this!
8) I'm willing to bet Asterion has a praise kink; it just makes sense to me. Either praising or being praised by MC sounds like something Asterion would be into.
I also think Asterion would be into leather and harnesses and the like, kinda leaning into his bovine heritage a bit.
Another idea, as mentioned before, would be body worship. Asterion has shown a great deal of pride in his physical form, so it would make sense that he would be interested in this sort of kink.
edits:
Grammar & typos
*More ideas for question 4