Swinging pendulum problem

I wanted to send a simple experimental file with three problems I cannot solve.

The file is as simple as I can make it (2 very simple, low res objects = 20 mb & 9 keyframes), but it won’t upload. So I guess I have 4 problems.

I want the stage to rotate around counter-clockwise using keyframes at every 45 degrees.

First problem. It rotates 180 degrees, then reverses and races around to its next keyframe at 225 before continuing. Why the reverse?

Second problem: when it gets back to 0, it pauses before starting around again.

Third Problem: I want the pendulum to attach to the arm and swing naturally as the stage rotates. I have experimented with Rigid Bodies, but can find nothing that works. I want the top point on the pendulum to be somehow connected to the point on the rotating stage arm. “Pinning” doesn’t seem availabe for Rigid Bodies as it is for cloth, and I can’t figure out how to use “Hooks” even though I have gone over the manual carefully.

Thanks for any clues you can provide.