My on-the-fly rulings:
If the invisible mount doesn't attack, and doesn't aid your attack (e.g. by charging) it stays invisible.
Your mount is generally one size step larger than you, which is roughly twice the size. So I'd say a 2 in 6 chance to hit the rider, and a 4 in 6 chance to hit the mount. For a much larger mount (e.g. riding a dragon) it might only be a 1 in 6 or even 1 in 8 chance to hit the rider.
invisible Rogue on an invisible chair - if the fighter is trying to hit the rogue, hitting the chair instead seems like it would count as missing the rogue - that is, as part of the % miss chance. How many ways can he miss? He could strike too high, or too low, or too far to the left, or too far to the right. Only if he strikes too low would he reasonably hit the chair, so call it a 1 in 4 that he hits the chair on a miss. The only reason to account for the chair at all is that the fighter's blow could smash it or knock it over, causing the rogue to fall (or at least make a Dex check to land on her feet).