Taxes and Fees and Award Stays

Ambassador Free night
As the certifiace only covers the second of a two night booking, you need to pay all taxes and fee for the first night. Usually not for the first night, but it depends on how the hotel charged the certifiace. Some divied the amount by two night and let you pay for two nights though the reduced amount. In this case you quite often have to pay taxes and fee for both days but on a lower amount. Except for amenity fee and resort fee there would not be a large difference as the taxes are a percentage of the amount. City taxes have to be paid usually on free nights.

Amenity Fee
Charged by the hotel and icludes certain things. It is not a tax in the legal use of the term but made by the hotel to cover for certain things by lowering the room rate. You could not avoid paying it if booking the room in most hotels. Some hotels charge it on award stay, some do not. You have to confirm with each hotel.

Cash and Points Stay
You are actually buying with the cast an point amount (see this post), therefore a cash + points stay is considered a point stay. Not taxes on the cash part of the room rate should apply, but city taxes and amenity fee could apply.

City and Local Taxes
Some cities / countries have local tourist taxes (e.g. France), which are added (see this post). In some German Cities (Frankfurt, Berlin) they are added for touristic trips. Those usually are even charged on award stays.

Resort Fee
Charged by the hotel and icludes certain things and amenities. It is not a tax in the legal use of the term but made by the hotel to cover for certain things by lowering the room rate. You could not avoid paying it if booking the room in most hotels. Some hotels charge it on award stay, some do not. You have to confirm with each hotel. In general those are more often also charged on award stays or free nights