Yes
Yes you have to have Xbox live to update your flash drive.
No, It will not save game memory.
You can format and use a USB flash drive as an Xbox 360 storage device and store up to 2 terabytes (TB) of content.
If it is compatible for Xbox 360 then you should be able to use it for the Xbox one. There shouldn't be any issues.
For Grand Theft Auto: V, there will be an initial install on Xbox 360 that will require an Xbox 360 Hard Drive or an external 16GB USB flash drive with at least 8 GB of free space. If using a USB flash drive it must be at least USB 2.0 with a minimum 15mb/s read speed and formatted for Xbox 360 use. A new USB flash drive is recommended to ensure optimum performance.
No because xbox do not have windows
yes it is
You can't transfer files on xbox 360 using a usb thumb drive, but you can if you buy a xbox 360 memory card
no you could use modio for your xbox 360 with a flash drive
You can.
yes, you can. you can copy music to the xbox 360
No, you cannot play Xbox 360 games directly on an Xbox console using a flash drive. Xbox 360 games must be played on an Xbox 360 console or an Xbox One/Series X|S that supports backward compatibility. Additionally, while you can use a flash drive for storing game data or saves, the actual game files need to be installed or accessed properly on the compatible console. For GTA V, it must be installed on a compatible console to play.