Learn Finnish: Luulen, että tämä loppupomo on kuolematon. - I think that this final boss is immortal.

It is formed from the verb kuolla (to die). To make the negative participle, you take the strong stem of the verb, which is kuole-, and add the suffix -maton. Literally, it translates as undying or immortal.

Does kuolematon function as a verb or an adjective in this sentence?

Here it acts completely as an adjective describing the noun loppupomo. Because the subject is a singular noun, kuolematon is in the basic nominative case.

I know ajatella means to think. Why is luulla used here instead?

Luulla is used when thinking means supposing, assuming, or guessing something to be true, often with a hint of uncertainty. You are assuming the boss is immortal based on gameplay, so luulen is the perfect verb here. Ajatella is used for the active cognitive process of pondering.

Is loppupomo a standard word?

It is a very common compound word used in video gaming contexts, made of loppu (end) and pomo (boss). Finnish gamers use it exactly like English speakers use the phrase final boss.