Please explain the second charged move feature.

It's really a lot simpler than you're making it out to be.

1. You're guaranteed one of the moves that isn't the current move.

2. Random chance.

3. It's guaranteed using a TM will get you the other move it didn't learn. In the event the Pokemon has more than 3 available charge moves to choose from then the new move will be random, just like if it had one move.

4. When you use a CTM it asks you which move you would like to forget. This is where you need to pay attention to your shit so you don't accidentally get rid of Shadow Ball on Mewtwo or something.

5. See above explanations. You get to pick the move to be forgotten.

6. It's random.

7 & 8. Both are available to you at all times.

Basically the new charge move will be different from the one you have & from its available move pool. If the mon in question has just 3 charge moves, then using a TM on either of the charge moves will give you the third move as you can't have 2 moves the same. If there are more than 3 moves in the move pool or you already have a legacy move it gets more complicated getting the move you want via a CTM & it's back in RNG territory. Once you have the two moves you want, both are charged up when you are attacking, in both raids & PvP. Once charged you can pick which to use. Which one charges faster depends on the move & how much energy it needs to charge.

This wasn't so clearly answered yet so:
8. Instead of one charge move button in the middle of the screen, there're two side by side. Both indicate how close to charged they are, according to their energy requirement.
Check a youtube video of PvP if you're curious to see it before trying it out.

7d) If a gym defender has two charged moves, the AI chooses them at random, subject to energy requirements (for example, a Gyarados with Hydro Pump and Crunch is unlikely to use Hydro Pump, but a Gardevoir with Dazzling Gleam and Shadow Ball would use each in about equal proportion, possibly both in the same battle).

One more thing, the second move is carried over through evolution. For most Pokemon it doesn't matter since the cost is the same for both the evolution and pre evolution Pokemon. The exception is for baby Pokemon, they all have a discount and cost 10k dust only. This means it's better to buy a second move on Togepi or Munchlax before evolving.