Also check your alternator output and your starter circuit. Breakaway brake system?
The solar should not overload the wire because the ampacity should be well above the solar rating. Really just protecting the wire from power coming from the battery. Yes if the controller is right there next to the battery IMO skip the fuse is OK. Several feet away or going through blind areas or anything else tricky about it then yes put a fuse close to the battery.
Also don't forget your battery interconnect fuses. One at each end.