Yes as long as you realise if you miss your connection you will have to buy another ticket to New York, why not see if the airline flying to New York also do flights from Manila or check on Skyscanner.com for prices
Of course it is OK
It's more expensive to fly here than from HK even if you combined the price.
If you book 2 separate tickets you run the risk of having a big headache if your flight to Hong Kong will be delayed as if you failed to check-in at HKIA at least an hour before your onward flight then you will pay a lot of $$$ as fees and penalties. You need to pass thru immigration and customs at HKIA then take an elevator up to the Departure area to check-in for your onward flight.
there are plenty airlines that offer promo fares to the u.s.: eva air via taipei. cathay pacific via hong kong. asiana or korean air via seoul. ana via tokyo. or pal on a direct flight. check when they have promos unless you cant wait anymore and need to buy. if your research still shows your original option as the cheapest way, then you decide what is best for you.