Hive Mind and Counterspell
Yes, you can. By the time Hive Mind's ability copies your opponent's Counterspell, that Counterspell is already on the stack. So you can choose it as a target for your own copy of Counterspell.

In more detail, what happens is this:


You cast your creature spell, which let's say is a Weirded Vampire. (Why would you be playing Weirded Vampire against Hive Mind? Weird, huh.) The stack is


Weirded Vampire

Your opponent casts Counterspell, and Hive Mind's ability triggers. The stack is


Hive Mind's ability
Counterspell (opponent's)
Weirded Vampire

The ability resolves, giving you a copy of Counterspell, which you can choose to have target the original Counterspell. The stack is


Counterspell (yours)
Counterspell (opponent's)
Weirded Vampire

Your Counterspell resolves, countering your opponent's Counterspell. The stack is


Weirded Vampire

The Weirded Vampire now resolves.


This does mean that (in a 2-player game) Hive Mind basically nullifies any counterspell which can target a copy of itself.