sürükler peşine aşkın: i rephrased it "(o) aşkın peşine sürükler" as a regular sentence, with the hidden subject "it," and missing object. "it" may refer to "the heart" in the previous sentence, although i'm not sure.
but if "aşkın" is taken for the subject of the sentence, then the meaning is something like "your love drags toward behind it." i don't know what this "it" refers to. also, drags whom?
if it were "aşkın peşinDE sürükler", then it would be easier to understand:
the heart drags/drifts one behind/after love. i listened to the song a couple of times. he insistently says "peşine" (or so do i hear it

).
alacağına saymak: i don't know the exact financial term here (i'm terribly bad at economics and economy related subjects and i still don't remember how i passed EC101.

). i give you an example and you give me the phrase.
suppose that i owe you $10. then i give you something to sell for me and you sell it for $30, but you give back to me only $20 and say "i keep this $10 for the money you owe me." so, you keep it as what?