You are going to have to seperate the supermarket and “car camping” as there is nowhere you can do both. Iains suggestion of parking at Burnside might work for the shopping trip, assuming you can get your shopping in a couple of bags. (The road up to Macdonalds is No Parking).
Ciste car park might work for your camping, though you’d have to be very careful about which direction you parked.
Personally, I’d head straight to Inverness and ride from there, booking into a camp site or B&B if needed. I’m not even sure that driving around with a non-working starter is completely legal 😊