I tried to be clever and put a tractor beam on the ship I was supposed to follow.

It turned hostile but didn't attack.
So I followed, but with auto fire it got destroyed when the actual enemies turned up.

Not sure if this was intended :D

It is intended. Following someone on the street and throwing lasso around their neck is not the same thing. :) Grappler is invasive methos of stopping someone from running away, thus he will turn hostile. ;)

One question about side missions.
If I mess up like this and fail, do I still get new side missions, they seem to build up on each other?

Sometimes going about 2 sectors away resets them so you can try that.