If the opponent plays Unchecked Power while I have Glasc Mixologist on the battlefield, am I able to play units from the discard to the battlefield Glasc Mixologist was on?

Yes, you are able to play a unit from your trash to the battlefield where your Glasc Mixologist died.

This interaction is confirmed by RiftJudge FAQ #10406. Here is the breakdown of why this works:

Sequence of Events

1. Resolution: Your opponent resolves Unchecked Power. Your Glasc Mixologist takes lethal damage and is destroyed.
2. Deathknell Trigger: The Deathknell ability triggers. Per Rule 734.1.d.2, it is added to the chain as a pending item before the unit is moved to the trash.
3. No Loss of Control: Even though your Glasc Mixologist is no longer on the board, you do not lose control of the battlefield because an item (the Deathknell trigger) is still present on the chain (Rule 187.4.c).
4. Chain Resolution: Because you still control the battlefield, you have the necessary permission to resolve the Deathknell effect and play a unit from your trash to that same battlefield.
5. Finalization: Once the unit enters play and the chain clears, you maintain control of the battlefield because you have a unit present when the cleanup completes.