6
TFL Bus Status Updates provide up-to-date information on any disruptions, saying what specific stop(s) are not being served and any new stop(s) that are being served as a replacement.
https://tfl.gov.uk/bus/status/
3
That seems tricky. Last train leaves at 8pm and last bus at 7pm.
Other options to consider:
Private car or Uber. Will cost you around 120 Euro. Uber may charge a significant "prime time" surcharge for New Years Eve, so you would be better of booking a private car up front.
Rental car for a one way seems too expensive, but may be an option of you ...
2
There is a 5 min grace period So Peak is from 635 to 927 And from 1605 to 1857
https://tfl.gov.uk/corporate/transparency/freedom-of-information/foi-request-detail?referenceId=FOI-1798-1718
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