how do i get the main characters like mao to learn more skills?

Do you mean weapon skills or unique skills?
If it's weapon skills you're asking about, you need to have them inherit the skills from someone in their club that knows them by going to the Class World.
If it's unique skills you're asking about, just level up.

It should be noted that Mao's final unique skill is obtained at a certain part of the game, not by leveling up.

I think it is available to use on the last stage of Chapter 6 and beyond....When Mao says he's like, bursting with power or something along those lines....

If I'm not mistaken, it's specifically after level 6-3.

i was talking about weapon skills