If you don't draw a card because all the draws were replaced (with dredge, for example), you still have to put a card from your hand on top of your library.

Paying cumulative upkeep is always optional. If it's not paid, the permanent with cumulative upkeep is sacrificed. Partial payments of the total cumulative upkeep cost can't be made. For example, if a permanent with "cumulative upkeep " has three age counters on it when its cumulative upkeep ability triggers, it gets another age counter and then its controller chooses to either pay or sacrifice the permanent.