Aye, short range it would only be used for, since long range, why not point at the enemy plane?
Regarding the counter for the plane's speed, that's a tough one. The missile would be even shorter ranged then. Not too effective. Maybe adding a secondary or primary mini-booster? For countering the jet wash, add an extra kick to the missile's detachment from the plane.
As for targeting, that's tricky, radar is too slow for dogfighting, and as you said, heat seeking is dodgy.