What values can the carry flag hold, and how to check its status in x86 assembly?

What values can the carry flag hold? Is it just 0x00 and 0x01 (boolean) or is it 16 (or 32/64) bits like the rest of the CPU registers?

How do I check its status? Do I just use it like a normal CPU register like cmp cf, 0x00 then jg <jump destination>?

I am writing a mini-OS. Is it good practice to use it for my own purposes, or should it be reserved for exclusive write-permissions for the CPU, and all I do is read from it?