Which services is it permissible for one to serve the opposite gender? (i.e. manicure, pedicure, haircut, massage, etc.)
In general, for matters of personal beauty, it is not permitted to serve the opposite gender.
For a man serving a woman, although we generally say that while “on the job” a person is “immune” to improper thoughts, this is not readily applicable to matters of beauty, where the job involves observing the other person.
A massage, which involves intimate physical touch, is certainly prohibited, and authorities generally write that the same will apply to giving a haircut. There is some room to debate the nature of a manicure and pedicure, but the leaning will certainly be towards stringency, in particular because there is no shortage or women who are able to offer the same service.
Please see here for further details and sources.
For a woman performing the services to a man, a similar prohibition will apply, and please see here for details.
Best wishes for a chag kasher ve-same’ach.