3. Spare him and promise to fight again next time. Would team up occasionally, with Asterius saying "The only one that could defeat you is me!"

That's what rivals in anime always do.

What role do you think this character will play in later stories?

Will spare him, probably what will author do at least since we need strong dudes for OEBD.

I think that Asterius and the rest of the Xenos would join Bell and his alliance as they head to the final floor of the dungeon. Having the Xenos join makes sense since Bell is doing it for them, and having the strongest Xenos fighting along side them all would also make sense. Whether or not he faces the OEBD would depend on which order they are faced. ie, if they face the dragon first I don't think Asterius would be there since they Xenos wouldn't be allowed to breach the surface. However if they take down the dungeon first and the Xenos becomes public knowledge it would make sense for Asterius to face the dragon too.

Another thing to note is that as Bell gets stronger the number of people he can effectively train with will go down. Once Bell hits level 7 it's likely that only Ottar would be a viable training partner. Ais and the rest would be able to help him to a degree as far as skill and tactics go, but their levels will be too low to give his status much of a boost.

Given that they seem to be setting up Asterius being Bell's ultimate rival and that enhanced species can grow at a very large rate I'd assume he will be level 8 when Bell finally faces him. Which will likely be how Bell hits level 8. Once that happens he'll leave Ottar behind as well (unless Ottar breaks through to 8 as well). If Bell spares Asterius he could also become a training partner for Bell as he continues to grow.

Asterius will obviously be killed by Bell... Asterius is a warrior so if he will be defeated he will choose to be killed by the opponent who defeated him.

@Yazmarohma - how about, Bell defeats Asterius, but does not kill him - instead, says some corny line like, "The best way to fully defeat an enemy is to make him your friend" then offer a chance for greater fights, for example against the OEBD. Because as you can see, Bell wants to save "everyone".

Well... Bell learn Ox Slayer skill so that means he killed Asterius. You cannot get that skill if you don't kill Asterius or other monster types.

Asterius is still alive so I'm not sure what you mean