1) The Shower Guru and I have observed this too and started using it on our runs, dubbing it the "PP Clip". We're still working on clipping through hazards.
2) I agree, it almost seems RNG where you go. But we've done testing on it and it would seem you're right, where you go it slightly dependent on what angle you hit the puddle. It's a risky strat using it in a run but looking to be viable, we've dubbed it the "PP Slide", as seen in Shower Guru's guide.
3) We've done testing to see if we can manipulate where the dads spawn but to no avail. Dads spawn on hazards, powerups can spawn on top of you, dads can spawn almost on top of each other, it's completely RNG.
4) We're still working on data mining for the game, we'll let everyone know if we find anything useful.

tl;dr gr8 b8 m8. i rel8 str8 appreci8 nd congratul8. i r8 dis b8 an 8/8.