According to the not-quite-canon* old Technical Manual impulse drives work by a combination of “mass lightening” and plain old thrust.
As for the stars zipping past in warp speed there’s a fan theory I like; that they aren’t actually stars but interstellar particles interacting with the warp field. Totally non-canon but at least it explains how you can see them thoguh a window at FTL.
In that on one hand it’s not officially canon, but it does seem to be followed on the show anyway. And it’s the best we’ve got, anyway. As much as I like it, in my opinion one of Trek’s flaws is that the writers never seem to have been willing to write down a “bible” for the setting and mostly just winged it.