Mr & Mrs Deemus -

I usually book this hotel through FHR, so can't speak for the Diamond treatment but have always received the FHR upgrade.

Regarding your questions:
1) my recent similar situation at (another) PH was that availability will ultimately drive the decision, so it will be tough if they are full on the 31st. You can give a try calling the front desk to check and put a note in the record that you would love it if you didn't have to change rooms.

2) New Year's in Istanbul - like any big city - is a bit chaotic, so a Bosphorus Dinner Cruise could be a nice solution. Keep in mind that the weather will be cold. Finding a taxi may be a problem on the return depending on the time so consider arranging having the hotel arrange one.

3) Taxis from the airport are generally legit, though they may not all know the PH by name given that it's on a small side street and not a huge property. Have a print out of the address and local area as backup. The will definitely know the area (prime shopping, but not so touristy).

PS - don't forget to get (ie pay for) your Turkish visa online before you leave! (assuming you are a US citizen)