A month post closing, the son of the buyer (mother) has written a "legal" request to have us buy him a new refrigerator.  

To legalize a curb cut in NYC, your first step is to hire a licensed architect or engineer.

I did that (posted the notice on the screen door and took pictures), however don't know if it's legally served. 

It couldn't hurt to call a couple attorneys right away to see what they say in terms of cost and suggestions for dealing with this quickly.In terms of mitigating any legal issues with your tenant be sure you are documenting every conversation you have had with the HOA in terms of asking them to make the necessary repairs.

If you are a legal property manager in your state the owner should have the unfettered ability to allow you to act as his/her agent to enforce the lease, whatever provisions they may contain plus whatever your state laws allow.

Maybe they've been burned by landlords in the past and are being very careful.You can legally reject them based on personality, facial tattoos, body odor, or other factors, but you better make sure you can prove that it wasn't based on any protected class like race, religion, familial status, etc.

I want to pursue the case without legal help but I fear she might use my email to double down on harassment claims and go for appeal.Really down atm so please advise :)

I don't try to evict based on neighbor complaints as those aren't super reliable and the people likely won't show up to court. 

If you fail to meet this deadline, I will file a complaint with the Virginia REALTORS."

When a lawsuit is started, there is something called the complaint.