Missiles can be relatively easily evaded by jumping slopes on tracks such as Tiny Arena. You also may be able to guide one into a wall by performing a sharp turn. Is there's any way to avoid being hit when on flat, open ground without items?
You can jump the missile when your timing is right (seen here). Look backwards when you get targeted to get a feel when to jump. With the lag in online this is nearly impossible to pull off.
If there are racers near you you can try to drive in front of them so the rocket will hit them and not you.
You already mentioned a sharp turn and this is also a good way. Just do a 360 by repeated jumping + dpad down + dpad left/right + holding brake which should be faster than getting hit and recovering, you won't even lose your reserves doing this.
Nope. Only thing I can think of is guiding them into items already placed on the ground, but that probably isn't the answer you're looking for. But without any weird online hit registration issues, a missile fired in a flat and open area should hit you. I think if they didn't, they'd be unsatisfying to use and much weaker as the target would be able to avoid getting hit by them in almost every scenario.