Question about Braun Spare battery Sony NP-F550

Yes - it is compatible. I have exactly this combination.

These batteries are available in different capacities. They represent a standard among video batteries defined by Sony. They are available with 2, 4 and probably also with 6 cells. All different sizes of the NP-F standard have the same form factor regarding the electrical connection. The NP-F550 is the smallest with 2 cells. With 4 and 6 cells they are built correspondingly higher, but this has no influence on the connection area. If the device is intended to be operated with NP-F batteries, these Dörr batteries should work, as they correspond to the Sony standard.

I don't know, I bought the battery for a video light.