Yes to all of those questions Kedi. There is a supermarket right near the Marina in PEK where you will be able to pick up most of the things you may need (including wine). A lot of the things you will recognise from home now that so much of our stuff comes from Europe. Incidentally, when I've been self-catering I've taken a few packets of sauce-mix, as they're easy and light to carry. There are a load of restaurants round the area, all doing nice food at reasonable prices, as well as a couple of more expensive ones. Prices are on the boards outside so you shouldn't get many nasty surprises!! Many of them do seem to cater for more of the 'international' brigade, with pizzas, steaks, pancakes etc. (and beautiful icecreams) but you should be able to find some more authentic Tunisian dishes. Go into Sousse and have a wander into the Medina for a taste of the real Tunisia. You can get fresh fish and meat there and bread which is still hot.
Those who know me on here may be surprised that I'm singing the praises of PEK when I'm a devotee of Sousse itself, but if you're looking for an apartment, rather than going S/C at an hotel, the best ones are certainly in PEK. Many hotels throughout Tunisia do provide self-catering, or bed and breakfast, so that might be another option,