Need to find someone in NYC to help look after my Parkinsons-having dad.

Although this clearly won't solve the problem of the 3 AM thing as they're only around during daylight hours usually. 24-hr care is nearly impossible to get unless he is literally incapable of caring for himself. There may be a nighttime care system, though, I'm not sure how home attendant hours are doled out.

Speaking as someone who recently lost a grandparent to Parkinson's: Whatever arrangement you find for him must account for the fact that this is going to get worse. He will fall more and more often, and eventually he will not be able to walk. Parkinson's moves slowly enough that you have time to get used to each new advancement, for it to become the status quo; it's easy to just deal with the new change and feel like the illness has been sorted, but then you have to upend everything again six months or a year later.

http://www.nyc.gov/html/hra/html/directory/home_care.shtml is the NYC portal for home care services. You'll want to look into "Medicaid-Funded Home Care" but you may as well look at the other options as well.

If you can get a daylight home attendant, the roommate may be able to handle staying which would perhaps solve the 3am issue.

Yes, you want a home health aide.

Is there any chance that occupational therapy would help him learn to use a cane or walker and fall less?

You definitely want a home attendant rather than a nurse. But also try to set him up so his apartment is less of a hazard. In NY having 24 hour care paid by insurance is rare and mostly limited to people who are truly helpless without another person like people with quadriplegia or who require home ventilators. Medicaid will pay for home attendants but Medicare does not. Of course you can always hire private aides or come to some barter arrangement like the one your father has now. Also, are there ways that your father's house could be made safer for him? Such as grab bars in the bath, a bath chair or bench, eliminating throw rugs, better lighting. Move any furniture in places that pose a hazard. If he had a bedside commode or even one of those little urinal bottles to keep by the bedside, he wouldn't need to get up and go to the bathroom in the middle of the night and could empty it in the daytime, eliminating the need for someone to go with him. Does he have LifeAlert or one of the other wearable alert systems? Finally, if you're doing all this at a distance, you probably want a geriatric social worker to help navigate the system. If your father is not already seeing a geriatrician, he should think about it. A good geriatrician can help strategize about planning for present and future limitations as well as helping deal with issues like medication interactions, which are a huge issue for elderly people with multiple health problems. Geriatricians in general are also just much more apt to be really nice and caring physicians than a lot of doctors.

Theora: He has those things (got them in rehab) and uses them but will occasionally get dizzy and collapse while using his walker. Elusive: He does have a lifealert and place to pee in his bedroom. He is very stubborn and reluctant to give up any independence (which was true 10 years ago as well) I will look into a geriatrician.

I have been dealing with a similar situation with my mother. I got her a life alert button which she uses when she falls. Then we set up some people (I bet home health would have resources for you) to come pick her up when she has fallen. We basically pay $100 per trip to pick her up. This can be a 15-minute operation up to two hours if she has knocked things down when falling. The situation is not ideal but it is working now. I also worked with her primary care doc to get her medications modified so that she doesn't fall as much and this has helped TREMENDOUSLY. Not really an option for you, sorry. Oh, and we had grab bars installed in her place in areas where she typically falls (right outside the bathroom door.) Keep in mind that as your father deteriorates, he will probably get to the point where he realizes he must change his living situation. Whatever supports you set up are temporary until he mentally gets to that point. Sorry for you. Find someone you can complain to when it gets tough (my poor brother has received many a lengthy email from me when I needed someone to dump on.)