Yes, that's all correct -- but note that you can't use an alternator to directly charge an LFP battery bank, unless it has an external field controller set up for LFP (e.g. Wakespeed -- installed cost getting on for a grand) or DC-DC converters in between (e.g. 2 x Victron Orion, a bit less than a grand) -- and in the second case you risk frying an alternator unless you add extra temperature sensing/current control circuits. To run the engine for only an hour a day will need a big alternator (e.g. 170A rated) with a polyvee drive, some engines have this fitted as standard or it can be added, others not so easy. You won't be able to run this at full rated output for long periods due to overheating, probably around 100A-120A is safe into an LFP bank. If you want to add power-hungry appliances like a washer-drier (like you said) then this will add extra constraints on the system, for example battery/inverter size big enough to provide the ~3kWh needed per load. And with only 1kWh/day energy coming in, it would take 3 days to make this back -- on top of running your other energy consumers, so more like a week in practice. As usual, the devil (and the cost!) is in the details... 😉
