Future Continuous

Hello.

If we want to talk about two different actions in the future, do we use 2x future continuous tenses?

Here is the example:

While you will be playing your games, I will be watching my favorite TV show.

I've got some doubts about this because I have found sentences which have confused me.

Can you tell me whether they are correct or not?

Here are the sentences:

1) While you will be playing the guitar I will sing. (why not "I'll be singing"?)

*(I think that there is used future simple because it is a promise. Am I right?)

2) I will play the game of chess while listening to the music.

(This sentence has confused me the most. It sounds a bit odd to me. I think this one is incorrect.)

Thanks in advance.