Is his rating a limitation to teach me?
As I say in this answer, "you are too fixated on rating". High rating does not guarantee coaching ability. Low rating does not preclude coaching ability.
Today the guy in our club who does the most coaching is rated about 1900. 50 years ago, the first time we played for the same club, he was rated about 2150. He has coached a surprisingly large number of the players in our region who are now rated 2100-2300, although they moved on to better high level coaches before they got to those levels.
It is always interesting to watch him play one of his former students. Is the student going to give him a draw for old time's sake? Or crush him? If they give him a draw then afterwards the coach in him will tell them why they shouldn't do that while also saying "Thank you!"
I need lessons not only in openings and endgames but in middlegame play. Should I search for a better trainer out of my club or it is enough that this coach train me?
We don't know the trainer so we haven't a clue. Probably the best approach for you is to have a trial lesson and see what you think. Did you learn anything? Was it worth it?
Taking a trainer is not like getting married. If you find it is not helping you then you can just stop and walk away.