It blurs the line between your business relationship. It may be that he is totally honest and forthright and all of these issues just fell under Murphy’s umbrella. It could also be that he sees ways to get around paying rent by “fixing up” your property, although that isn’t the arrangement you were looking for.
Find yourself a local and reputable service company (check homeadvisor or angies list for reviewed companies!) and tell your tenant that while you appreciate his help, you are now in a contract with a company and need all repairs to go through them. Be clear: no deductions will be made to his rent for anything (put this in writing) unless YOU pre-approve it. You didn’t hire him as a handyman, you are his landlord and expect to make your fair profit for renting the home to him.
If the issues and un-approved deductions suddenly disappear, then you might consider the odds in favor of him being a not so honest tenant and give him that “out” to leave when you find a suitable replacement.
Above all else – stay positive! It’ll work out. Your tenant odds of good ones 2 out of 3 is not bad at all ?