As long as your club is running the POTD or an EC party like cat cafe or Dog Star, you should be getting your hunt drops from there.
Yes, hunt drops from parties and cash payout increase as ur cs increase (make sure you're at max plunder, i.e. total tut worth shd be 15m/1kcs or 15b/1mcs). Also, as ur cs increase, the no. of hits you'd need to get max party drops will decrease
I worked out my Max plunder 116 x 15m = 1.7b but I have 3.9b and my plunder can still go higher? Has the 15m changed?