Can I use a standard USB flash drive with Time Machine on my MAC Mini?

Flash drives have limited number of writes.. much worse than say SSD.

The way Time Machine works a lot of files are written over and over to the target. People find the USB type flash drives fail after a year in this sort of setup.. and they are not so cheap for large sizes.. you are far better off using 2.5" USB drive for this task..

Yes, assuming that the drive is formatted correctly in HFS+, also known as Mac OS Extended (Journaled).