Starting with your arrival into SIN from HND at 0655 ... you are correct you cannot check through your bags if you want to fly out on Scoot. If you fly Vietnam Airlines, then you can stay airside and go to the transfer desk and ask them to put your bag(s) from the HND flight onto the one to HAN. Read this
Transit time / procedure on two separate tickets for Changi
Assuming your inbound is on-time, you should have enough time to go through immigration and collect your bags and re-check with Scoot. SIN is a very user-friendly airport.
You have no airline lounge access on the basis of your NH ticket.
On your return, it depends on who you are flying with - Scoot or Vietnam Airlines? If the latter, you again go to the transfer desk and show your NH ticket and ask for bag(s) to be transferred. Then you should spend a couple of hours in the Transit Hotel. You should book in advance. One of many threads on this topic
Which Singapore Changi transit hotel?
If you arrive on Scoot, then things become less easy. You will have to go landside, pick up your bag(s). You don't qualify for
Scoot-thru. You can't re-check them at midnight as the NH check-in is not open and you can't get airside again as you need your NH boarding pass stamped to get through security. Changi is open 24 hours ... there are several restaurants and coffee shops open in the departures hall where you can wait for NH check-in to open and then go to the lounge.