Standing and fighting
Yes, easily handled.
Moving around an opponent while fighting
Handled moderately well, although suffering a penalty of -10 for walking five feet to circle around an opponent is kind of rough.
Swinging at an opponent while chasing him
For point 3, that would mean "react and melee", or, if you manage to get adjecent to your opponent at some point, "press and melee". If he's faster than you, obviously no attack is possible.
I disagree, the RAW don't handle this one at all. If you need to move more than 40% then you cannot attack. Thus, as long as your opponent can move as half as fast as you can, he can avoid being attacked. Sure, you can kick up the pace to get an attack in, but so can your opponent. As a result, unless you are significantly faster than your opponent, he's going to get away. Cinematic, perhaps, but frustrating for players!
Swinging (once) while moving past an opponent
Point 4 I'd handle by move in snap, attack in normal, then move in deliberate (or "disengage from melee')
First, the rules don't really specify a penalty for choosing a move action rather than a disengage from melee action. But, that's really a different thread. Let's assume that once you're "in melee" you must use a disengage action to leave melee. Then, a charge attack becomes: Move at most 15%, attack at -40, then disengage 25%. At a Fast Sprint pace (lots of exhaustion points gone), that's 30' of movement + 10' for the disengage, all for a charge attack at -40. (If we throw in SoHK, you can get half of that back, or all of it with a pole arm. I.e., even with SoHK charge bonuses, a charge attack is rarely worth the effort.)
Fighting while engaged in "forced" movement (flying/downhill skiing), i.e., you will move or you will crash/fall
if I allow this, why can't I attack ALL foes along my path
The rules are very unclear with respect to flying. If a flying creature can remain aloft for 0% activity, then flying creatures can all hover (a feat most birds cannot accomplish). Thus, it would seem that a hawk (or other similar creature) is forced to use the charging rules in the previous case.
With respect to attacking everything along one's path, the same issue arises if you allow mounted combat. When two knights ride past each other, they both (presumably) get an attack, even though there's only one "swing" involved. We can claim that the mount is doing all of the moving, but is that much different than gravity providing the movement when standing on a slope with skis on your feet?
Fighting while maneuvering, but not moving (climbing/swimming), i.e., a maneuver is needed to stay in place (hanging on to a rope/treading water)
And, the rules are also not clear how to handle these situations at all. Perhaps such maneuvers require only a small amount of activity (e.g., 20%), but that runs counter to the RAW, which indicate that climbing and swimming require (IIRC) at least 50% activity.
Not that I have great suggestions. Just that the RAW are (IMHO) overly restrictive.