Regarding a supermarket there is a the Starling almost opposite the Almond drive, very well stocked, also a pharmacy opposite the supermarket with a lovely helpful fluent English speaking lady pharmacist. Definitely hire a car to explore places like Salamis, Karpaz, St Hilarion etc. As already mentioned below they have their own fleet of hire cars. They are, like the hotel impeccably well maintained and clean!
Hi. It would be a long walk! No, its about 8miles from the Almond to Kyrenia centre. You can take the dolmas (public bus) which run regularly and costs about £1. But, really, you need a hire car (Huda at Arizona car hire is great) if you`re at the Almond as everything is fairly spread out.