It looks like you’ve created a partition for Linux - you need to delete this partition. Leave it as “unallocated” or “free space”. Then the Fedora installer will see it as space it can install to. The installer will handle creating the actual partition.

The quotes are there because there’s spaces in the file name. You don’t see them in the GUI because they’re not actually there. They’re added by the ‘ls’ command to help with copy/pasting of file names. You can add ‘export QUOTING_STYLE=literal’ to your ~/.bashrc to permanently suppress them, or just do ‘ls -N’ as a one off.