You pool mine, difficulty goes up so your cut of the pie goes down. It is that way with nearly any coin. So responsive because you are asking obvious questions.

There is no "pile" of work, no "time left for next block solve." It is entirely random, being that each guess (share) is totally independent of any other share. You either find a share high enough to submit as a pool share, or you don't. The pool tracks the rate at which you submit shares to calculate your hashrate to verify that you are actually contributing to the pool and that you do have a chance (no matter how small it is) to solve a block. Whatever info that is in that share is all but useless for anything but verification that you are working on mining doges and nothing else.