Student or Learner
Any special strategy / scheme / offer your gym has implemented to retain existing customers
your gym has...or your gym have?
What reasons members give who do not renew their membership?
What all programmes your gym offers/offer?
What programmes does your gym offer?
If we are addressing an organisation that owns a number of gyms, the question would be:
What programmes do your gyms offer?
In affirmative sentences, it is the full verb that takes the -(e)s ending:
I work - he works; I offer - she offers; they play - it plays.
In negative and interrogative forms it is the auxiliary DO that takes the -(e)s ending:
do I work? - does he work? I don't offer - she doesn't offer; don't they play? - doesn't it play?