So let me see if I'm getting this right.
Avoidance is instant, which means once it is cast the spell itself is spent, so the effect will last indefinitely until it is triggered, rather than the normal 10 minutes, and cannot be dispelled in the meantime. (I take it you read Avoidance to read that the attacks must occur within the same round, not literally at once as the text states.)
Counter-Defense is not instant meaning it has a duration of 10 minutes, activated or not, it can be dispelled, and will continue to give you an extra defense every round until the duration runs its course. (Although, I'll be honest, fires off implies to me that it's a one time thing, not something that can repeat itself for a 10 minute duration, same with Counter-Attack).
As for Flying Kick, I'm afraid I don't see the correlation between instant spells and not being non-variable. Dragon's Breath is both non-variable and instant. Also, the spell says how far the caster 'flies', so I'm not sure that's a good reason for it to not be instant. Actually, if I'm following the string of logic being laid out here, then as written it has a duration of 10 minutes and during that time you can make a jump kick every round for your movement, which would also mean that you get a free attack unarmed attack every round on top of a regular attack since it's part of your movement, which is actually pretty cool. However, if that's the case, it is no way clear.
I'm pretty new to BRP and Openquest, but based on the text of the book I've got to disagree with you about Fist of the Wind and Multi-Attack. They say you get 1 extra attack per magnitude, not one extra attack per magnitude per round. Also, they're instant, which would imply the spell itself doesn't last and thus can't have a duration, and I'll be honest, it would be an awful low power point cost for violating the action economy so severely for 10 minutes.
Maybe I'm just being thick, but I think the battle magic section of the rules has a real clarity issue.