If you choose to pay the impending cost rather than the mana cost, you're still casting the spell. It goes on the stack and can be responded to, countered, and so on.

If you choose to pay the impending cost of a creature spell, it's still a creature spell on the stack. You can cast that spell for its impending cost only when you could normally cast that creature spell. Most of the time, this means during your main phase when the stack is empty.

"Impending N–[cost]" is a keyword that represents multiple abilities. The official rules are as follows: (a) You may choose to pay [cost] rather than pay this spell's mana cost. (b) If you chose to pay this spell's impending cost, it enters the battlefield with N time counters on it. (c) As long as this permanent has a time counter on it, if it was cast for its impending cost, it's not a creature. (d) At the beginning of your end step, if this permanent was cast for its impending cost, remove a time counter from it.

You may return any non-Avatar creature card or any planeswalker card from your graveyard to your hand with Overlord of the Balemurk's last ability, not just one you milled while resolving that ability.

If an object enters as a copy of a permanent that was cast with its impending cost, it won't enter with time counters, and it will be a creature.