Hi Yooou,
How can I apply resin to the sleeve? Using brush? Dipping?or Spray?
I would suggest that brush application would probably still be best. Dipping might work, providing that you agitate the braid enough whilst it is in the resin, so that the resin can wet the fibres thoroughly. Spraying would probably not allow the fibres to wet-out properly so I would avoid it.
To get a nice finishing, what should I do with the surface of sleeve after it cures? As you said, would a spray gun make the surface smooth?
It depends what sort of a finish you want. If you want a smooth, glossy finish then it might be worth wrapping the sections with release film or shrink tape whilst they are still wet to make them less textured once they are cured. After this, you could flat them back and then either lacquer (clear coat) them or paint a layer of epoxy coating resin on them, before flatting and polishing that.
If you actually want a textured finish then you could just leave it in its natural state or spray lacquer onto the braid and leave it.
--Matt