Learn Italian: Anche se soffro, voglio provare. - Even if I suffer, I want to try.

You are right that many similar conjunctions (like sebbene or nonostante) trigger the subjunctive. However, anche se (even if/even though) is a notable exception! It almost always takes the regular indicative mood, which is why we use the present indicative soffro instead of the subjunctive soffra.

Could I use cercare instead of provare here for 'to try'?

Not easily in this exact structure. When used by itself to mean 'to make an attempt' or 'to test something out', provare is the best choice. Cercare (when it means 'to try') is almost always followed by di and another verb, as in cercare di capire (to try to understand). Since the word 'try' ends the thought here without another action attached, provare is the most natural choice.

Why is there no preposition like a or di between voglio and provare?

Volere (to want) is a modal verb, just like potere (can/to be able to) and dovere (must/to have to). When a modal verb is followed by another verb, that second verb stays in its infinitive form (like provare) and connects directly without needing any linking prepositions.