Learn Turkish: Dinleniyorum çünkü yorgun hissediyorum.

No, çünkü is very straightforward! It works exactly like "because" in English. It simply sits between two complete sentences to link them, without changing their internal word order. First you have "I am resting" (dinleniyorum), then çünkü, and finally "I feel tired" (yorgun hissediyorum).

Is dinleniyorum (I am resting) related to the word for "listening"?

They look very similar, and beginners often mix them up, but they are different verbs! Dinlemek means "to listen", so "I am listening" is dinliyorum. The verb in this sentence is dinlenmek (with an extra n), which means "to rest".

Where does the double 's' in hissediyorum come from?

Hissetmek (to feel) is a compound verb made of the noun his (feeling) and the helper verb etmek (to do/make). When these two parts join together, the s doubles. Also, notice that the t in etmek softens to a d because it is followed by the vowel of the -iyor ending.

Could I just say "because I am tired" instead of "because I feel tired"?

Yes, absolutely! In everyday Turkish, it is actually much more common to say çünkü yorgunum (because I am tired) rather than using the verb "to feel". Both mean essentially the same thing here and are grammatically correct.