Unplaytested Suggestion: Fold Climb and Swim into a single skill, called Athletics, which would be Str-based.
I would further consider folding Jump into this skill, as it was originally Str-based. Then Escape Artist could be folded into Acrobatics, which means each of the new skills would subsume three old skills, which has a nice symmetry to it.
I would also add a feat that would allow a Dex mod to be substituted for the Str in Atheletics.
By folding Handle Animal and Ride together, you get a skill which is very often raised in tandem anyway.
Climb + Swim, while slightly unrealistic, makes a convenient game mechanic. Your idea of a Dex-substitution feat sounds like a good one, which I might houserule if Paizo doesn't make one. Thanks!
Handle Animal + Ride is a no-brainer. Why they were ever separate is beyond me.
Acrobatics as Jump + Tumble + Balance is probably enough; I'd keep Escape Artist separate, but make it apply to tying people up as well (see thread on "Use Rope").
Because you don't ride every animal.
I have to admit that your point totally escapes me. To ride an animal, you have to handle it. There's no way around that.
I have DMed several games with these changes (including Jump in Athletics, by the way) since before 3.5 came out. It has worked wonderfully.