I stayed in a hotel I wouldn't particularly recommend, but it was self catering with a kitchen just in case I needed to cook for myself. Provisions I brought were builders bars, trek bars, primal strips and wheaty sausages. I easily found vegan bread in a Lidl supermarket - just had to get a loaf labelled in both English and Greek and compare with the Greek text on other loaves to find the milk-free ones. Also picked up pickled gherkins, olives with lemon and one of those middle eastern roast veg pastes in a jar. We always had this stuff on hand for emergencies/picnics. I often found food labelled as suitable for vegans in supermarkets. Cyprus is remarkably overrun with British expats, so there was plenty of UK food in shops had I wanted such a thing. One small supermarket on a tourist route had as much vegan milk on sale as any large supermarket in this country.
Restaurant-wise, I stayed in Paphos which amazed us by having a Pizza Express, and we went there a couple of times because we like their stuff and were lazy. Sadly, it was no cheaper than back home. Also had some terrific food at the Syrian Restaurant in a back street in Kato Paphos. The waiter thought our diet was weird, but was very friendly and brought us some well-made meze including hoummous, roasted pepper with walnut and baba ghanoush to have with our flatbread and tabouli. There was enough left over to take with us on a beach picnic the next day.
Everyone I spoke with had perfect English so asking for vegetarian without milk was no problem. This included the visitor canteen at Kykkos Monastery which turned out to have rather nice pilau rice with lentil stew as well as a salad bar - a surprising feast to find on top of a rather remote mountain. Also had a really excellent meal at a new Indian place on Tombs Of The Kings Road called Koh-I-Noor. Special mention should also go to the Segafredo coffee shop near our hotel in Posidonos Avenue, Kato Paphos which had soya milk and vegan chocolate, was open from early morning to late night and had free wifi. Again though, London prices. On the seafront was Pahit ice cream shop with 10 vegan sorbets including chocolate, but at half the price of places like Scoop in London. They even had vegan chocolate waffle cones and various toppings. Pretty awesome.
In terms of visible animal abuse, this was surprisingly rare. I saw only one place offering donkey rides, though this was in the off season. A couple of places I saw goats grazing in the hills. There are loads of seemingly autonomous cats and also some little dogs that roam the city and countryside. Clearly the cats have clocked that tourists will feed them. At the tourist info centre, there were flyers for an animal sanctuary that seemed to be run by Brit expats again, and there is a donkey sanctuary in the Troodos Mountains.
In terms of stuff to do, I reckon hiring a car is pretty essential, and it meant I got to explore the mountains, the coast, lots of archeological UNESCO world heritage sites and a couple of monasteries. On the down side, I got a patriarchal vibe off some Cypriot men - for example one invading my personal space at a petrol pump with his huge belly. Also, we were there during the Presidential election when a pro-austerity Conservative got elected and we had to put up with an evening of Conservative voters driving through the streets of Paphos waving flags and honking. I imagine this time next year many of them will have been austeritied out of their livelihoods.