I think you got it almost right.
'부려먹는 중' means '부려먹다ing'
And '부려먹다' is a verb that means 'to make someone work hard for you in a way that's certainly unfair.'
If you make Jack do all your homework and don't give him anything in return, you've clearly done what I described above to him.
'진짜' means 'really'
'알차게' means 'productively' and in that case it's used to add some 'sarcasm' to the sentence.
Hope that helped