Learn Turkish: Sabotaj yapmalarına rağmen proje bitmedi. - Despite them committing sabotage, the project did not end.

It breaks down as yap (do) + ma (short verbal noun) + ları (their) + n (buffer letter) + a (dative case). The word rağmen (despite) always requires the dative case on the word right before it. So literally, this structure translates to "despite to their doing."

Could we add onların (their) to the beginning of the sentence?

Yes, but you do not have to. The possessive suffix -ları in yapmalarına already makes it clear that it was "their" doing. Adding onların (onların sabotaj yapmalarına rağmen) is grammatically correct but would just add extra emphasis to exactly who was doing the sabotage.

I see -ma / -me used twice here (yapmalarına and bitmedi). Are they doing the same thing?

No, they are different! The -ma in yapmalarına creates a verbal noun, turning the verb "do" into the noun "doing". But the -me in bitmedi is the negative suffix, changing the past tense verb bitti (ended) to its negative form (did not end). They look similar but serve completely different grammatical roles.

Why is the verb bitmedi (did not end) used instead of bitirmedi (did not finish)?