Disconnecting Bathroom Sink

Hi, I'm having my bathroom countertops and sinks replaced and the company doing the installation doesn't handle any of the plumbing work. To save myself a bit of money and not have to deal with scheduling two appointments with a plumber, I'm dismantling the sinks myself (but leaving the reinstallation to a professional—I know the limits of my abilities!). The first sink went fine until it came time to disconnect the drain pieces (forgive my ignorance of correct plumbing verbiage).

I've attached a photo to illustrate what I'm dealing with. I assumed that loosening the copper nut at the top would allow me to remove the drain tubing. However, when I grasp and turn the nut, the threaded portion as well as the gray tube turn with it. Is that supposed to happen? Should I continue trying to free it that way? If not, what's the best way to handle this?

Also, on another sink, I encountered a problem trying to loosen the plastic locknuts on the faucet stems. On the first sink, the nuts had some raised sections that gave me something to push against to loosen and remove them. On the second sink, it feels like whoever installed them broke off those pieces, giving me nothing to brace my fingers against. Any suggestions on a good tool or technique for loosening them?

Any advice is greatly appreciated!
Snib

If you’re getting new faucets just disconnect the supply lines and leave this nut loose on the drain. The countertop guys will dispose of the countertop w/ the old faucets attached

Thanks for responding. I'm not getting new faucets, and the installation guys will be hauling away my old countertops so I have to remove everything I'll need to reconnect them.

To clarify, I didn't have a problem loosening the white nut at the bottom. It's the copper one at the top that I'm struggling with.

Get your self two [pairs of channel locks put one the gray pipe to keep it from turning and the other on the brass nut to loosen it .