1)
For sexual positions, there's the typical bedroom play and positions.
Cowboy, press, missionary, Legs Up, Legs wrapped around.
More uncommon positions could work too. (I.e. ass up while the top drives down while standing.)
But since they seem to have their own private room, there's no reason to keep it there.
Open things up to having sex on the couch, shower, or against the giant window. Since the MC and Asterion can alter the hotel or summon things at will, getting proper support for aerial positions wouldn't be difficult either. Why fuck on the bed, when you can fuck on the ceiling?
As for kinks to explore, there's a long list that can probably work without being too uncomfortable considering Asterion's past.
Orgasm Control/Denial/Edging (torture of another kind), role reversal (Asterion being King), outdoor sex (assuming they can lock the door to the roof to allow Asterion to get naked.), and if it doesn't break any rules, virtual stimulation. (Vibrator the MC can activate at range.) Assuming more of a bottom MC, you could even use double-ended dildos or similar toys.
2)
Assuming we're talking bedroom only:
Asterion seems to enjoy light physical touch and warmth. I'd assume massaging him with heating oil or other sensory oils might help. Grinding and tail play would also work. As well as the dirty talk. Also wrestling. He seems to really enjoy the physical activity.
If we're allowing teasing outside the bedroom:
The typical standbys work. Quick pinch of the ass. Excitement about the night. When they stand the MC's hand could drift down towards his tail or ass.
3)
Asterion has a way with words, so the dirty talk and dirty poetry would likely be part of his attempts. As would kisses drifting towards the MC's lower areas. There's also the flat out greeting your partner naked when the MC walks through the door and carrying them to bed.
This is a little more difficult as these will all have to account for every player.
4)
Saunas are good ideas.
Adding a spa or public bath would be similar and allow for a more open experience.
Repairing or updating the washroom facilities for the gym would give an opportunity as well, giving them the idea for a shower scene in the bedroom. (Since I don't believe Asterion COULD shower publiclly.)
Night Club, especially if Luke is the first character. An actual strip club may be too much, but having a place for dancing that leads to the both the MC and Asterion getting riled up might work. If we want to go full porno, you can even have them have sex in the bathroom stall. (Though the stalls would need to not have any gaps.)
Movie theater/Drive-In can work too. MC can toy with Asterion over his clothes since the rules are in place. Heavy petting is on the table at least.
5)
That'd fall under roleplay or most "clothing" of the bdsm persuasion. Considering his past, a lot of roleplaying in that kind might be either outside his cultural knowledge (naive farmboy) or out of his comfort zone (sensory restriction and or pain play of any kind). Especially if the roleplay has a more subservient connotation to it. (Butler/Maid)
Body morphing or modifications might be under that umbrella too. While light stuff like piercings seems okay, having it come from the MC might come across as off-kilter.
6)
For teasing by a more dominant MC, I'd say fiddling with his tail when they stand together, instead of the typical arm around the back.
There's also pulling him along to the bedroom by his nose ring, assuming it'd been okay'd.
7)
If the MC hasn't been particularly dominant, I'd prefer to see Asterion being more assertive in that he wants this. Being the one to initiate the encounter. This can lead to full on power-bottoming, if that translates well into the scene.
There's also possibilities for more... tender scenes as Asterion attempts to have the MC get more comfortable.
8)
Kinks Asterion would be into would be more about his physicality. Body worship, compliments, and spooning. Wrestling and physical activities would definitely be something he'd enjoy.
He also seems to have a thing for scent.