He would need to be Gas Safe registered to work on gas as above but so long as he is insured and carries out his work in a 'Workman like manner', complies with all the relevant regulations, standards and instructions, I can't think of anything he can't 'legally' do.
The qualifications come in when, for example:
You have to join something such as a competent persons scheme (CPS) in order to notify work that requires notifying.
Situations where people will require them e.g. Schools, Nursing homes, Hospitals etc but if he is only doing domestic work I can't see them asking.
I know our insurance company never asks for evidence that we are qualified to carry out the work we do but that doesn't mean they won't if something goes wrong, so I would be cautious with thinking your insurance company will cover his work.
Always worth getting it in writing where sub-contractors are concerned. Better still, ask him to insure himself and look at it when he gets it.
Qualifications (decent ones) prove you have studied and learnt a subject to a certain level. There are many things in this job as well as others that you learn during the time spent in college or in an apprenticeship that you didn't know before and wouldn't know, had you not been shown. Some of those things are important and not knowing them can lead to disaster. Just because someone is good at DIY and works neat, doesn't mean that they are doing the job safely or correctly.
Hope this helps.