Opening tubes to unclog bathroom sink
PVC screw fittings are unscrewed in the counter clockwise direction, but that's in reference to the pipe they are attached to. You may be upside down in some of those connections.
The popup drain connection is made to the sink drain tail piece. You don't need to remove this to gain access to the trap below, so it can remain untouched.


Note that most clogs can be easily cleared by running a plumbing snake down the drain. You'll want one sized for your pipes, which in your case will likely be a relatively small diameter snake that can get around the drain and not get jammed in the tight turns of the trap.