86 camaro install

The wire that is getting power all the time is the one you want to hook up to your head unit's constant power wire (usually yellow).  The one that loses power when the car is off is the one that connects to the head unit's switched power lead (usually red).

Unless you really really want the illumination/dimmer features I'd just tape off those wires and not have them connected to the vehicle's wiring.  It's sometimes difficult to tell which one is which, and if you get the wrong one you can damage your head unit and/or the vehicle's electronics.

As for this inline fuse, which wire is it on?  If it's on the wire that has the switched power, then that's fine and you're good to go.  Just do your connection after the head unit.  The fuse is just there to protect the head unit.  Now if it's on the constant power wire it'll probably be no problem but if it's like a 5 amp fuse then it's possible your aftermarket head unit, if turned up very loud, will draw more than 5 amps and thus blow the fuse.