Transport: Haneda-Shinjuku

im heading to tokyo this nov.
my flight will arrive Haneda at 2305hrs.

need to check a few things.
1)what transport am i able to take at that time? If by train, what time would be the last train?
2)if by taxi, roughly how much would it be?
3)any idea which hotel allow check in during that time in shinjuku?

what transport am i able to take at that time? If by train, what time would be the last train?

According to the current timetables, the last monorails and trains leave around midnight, so you should probably be able to catch them. Considering the late arrivals, maybe new late-night trains or buses will be introduced, although I doubt it (especially in case of train).

2)if by taxi, roughly how much would it be?

To Shinjuku? Around 8000-9000 yen, I believe.

any idea which hotel allow check in during that time in shinjuku?

I believe that the major hotels like the Keio Plaza, Hilton and Hyatt will allow check in after midnight. I recommend to inquire.