hi i use a 300w inverter in my camper for lcd tv's , laptops,phone etc. there are two types of inverter irrispective of wattage. the cheapy, like the ring are modified sine wave type whereas the more expensive are pure sine wave[suitable for all needs],

you will need to check the needs of your appliance to avoid damage, the ring [what i use] will do most, caravan/ camper forums are good for your appliance info

it's all down to capacity yes charging during the engine running should be ok most laptops use 80w you 'lose' 10% [heat etc] so about 88w. i do not know how long your battery alone will remain useful when not running, why not try it before venturing out into the great unplugged wilds


all the best