GeezerCouple

We are thrilled to have J seating on this l-o-n-g trip in November, and it will be our first time on SQ, connecting in SIN, and arriving in AKL (for a cruise to SYD, flying home on CX).
These are awards tickets in case that affects any answers.
This is our first time to the area, including all of the flight route.

The outbound flights are:
First, we'll be taking a short flight into EWR the evening before, and then...

SQ 21 (EWR - SIN; 09:45, arriving 17:15 the next day)
connecting to
SQ 281 (SIN - AKL; 08:45 - 23:35 both that same "next day").

We will no doubt be totally exhausted after that long flight.
[Important: The only other really ultra-long-haul flight was approx 2 years ago, 14 hours to Japan. We both had *serious* jet lag, and I especially was a mess, disoriented, etc.; DH was a bit better. We both slept for 36 hours almost straight, getting up once to have a breakfast, and then again later very briefly for a light supper using room service. THEN I was okay...! Yes, we are meeting again with a travel clinic doctor to try to address this.]
So we think we should get to a hotel ASAP, get a nice (room service?) meal, and get to sleep, given we have another long flight the next day, with very early start/long day.
Is there a SIN hotel airside, and if so, can we avoid going through immigrations /etc., and then also avoid security again the next morning?

Now: Seating on these two flights... we prefer to sit in middle pairs so we can travel "together", etc., whenever possible if there is 1-2-1 seating. (With 2-2, a window aisle is perfect.)
I've read on SeatGuru that these J seats may have awkward foot wells, except for bulkhead, which have full width foot space. If so, we experienced something like this on Delta One, and the extra foot space in the bulkhead was indeed much more comfortable.

Any other suggestions about seating choices (if we can get them) on the two flights, or about the overnight between the two flights?

Many thanks!

GC