Fixing/replacing the starter shouldn't be all that expensive, aside possibly from the labor of getting at the starter. On the 4KY (I'm not sure if that's what this is, or if it's some other basic design) it does usually require removing the generator from the RV to get at the starter as it's on the back side and the full top cover must be removed, not just the usual service panel.
77rollalong correctly describes the wires and the (lack of) effect on your shore power connection.
Whether it's sensible to replace the generator with solar power and batteries really depends on your usage scenarios. If you need the generator to run air conditioning much, then solar likely won't be a viable alternative and you'll use your portable generator for that quite a bit, and have to deal with the noise and hassles of fueling etc. that it involves. (Unless the new generator is an inverter generator, it's almost certainly louder than the built-in generator.)
On the other hand, if the generator is primarily for charging the house batteries and maybe the occasional bit of microwaving, a solar install with a decent battery bank and an appropriate inverter could be a decided improvement.