I'm pretty sure the first one isn't possible, but I'll ask anyway.
1) Is it possible to have the BGM stop when the RMXP game window is inactive and then start where it was again once the window is active again?
2) Is it possible to have all events continue when the RMXP game window is inactive?
(Example: Conditional Branch, every 200 frames, 300 gold is obtained)
If it is, please tell me how, if not, well, then you can't tell me how.