How will I ever be sure that I will get the value of my burned BlackCoins back??
No guarantees.
I read on poloniex "BLK will be delisted on August 2. You will have until that date to trade relevant pairs on Poloniex, and up to and including September 2 to withdraw your BLK."
Does that affect when the burn will start or end at all?
Unlike snapshot, burning does not depend on exchanges.