Should be minyanim at Chabad. There may also be a frum group staying at the Kosher hotel that is a 5 minute walk from Chabad. Name of the hotel is Mikes Kanarium.
You can get Kosher food at Chabad. They have a proper sit down Flashig restaurant and also a Milchig Cafe with shakes, toasts etc'.
You also may be able to get food at the Kosher hotel.
I found Larnaca to be a very boring city so I'm not sure what there is to do there at all. They have a beach, scuba diving, water sports etc'. Most of the stuff is walking distance from Chabad so no need for a car unless you are leaving the city.