Solar fusing question

The purpose of the fuse is primarily to prevent the wire from overheating due to excess current. The battery is capable of putting out a whole lot of current; the solar panels are by nature basically self-limiting (i.e. their short circuit current is comparatively modest), so provided the wire is sufficiently sized there's no safety need for a fuse in that part of the circuit. It looks like the short circuit current for 24V 300W panels is typically around 10A, or 20A total; the wiring you have could carry that all day without problems. It can sometimes be convenient to put a fuse or switch or other ready way of disconnecting the solar panels for maintenance, etc., since many solar controllers should not have the panels active with no battery connected. It saves having to go up and cover the panels with something opaque or waiting until night to do stuff.

The fuse should go as close to the power source as possible, and be sized according to the wire size and connected equipment. If the wire is only for the solar charge controller connection, a 30A fuse and sufficiently heavy wire would be a reasonable starting point. A bit larger would also be okay, in my estimation, assuming the wire between the battery and the charge controller is heavy enough for that to be safe.

If the fuse is also for the connections to the rest of the RV, there's no way to even guess at an appropriate size without more information.

No fuse needed on the panel side. Nothing will happen if these short.
On the battery side you should have a fuse close to the battery and within 18” rated 125% of the controller max.