I have a partial answer to some of the questions.
1. Stray dogs and cats are the responsibility of the local authorities. They will have to take care of them, particularly they will have to chase them from or take them away from the neighborhood of hospitals, schools, sport centers, highways, ports and airports. There are about 300.000 stray dogs in Greece. Some are adopted, some are taken into a shelter for a while, the rest will stay on the streets and in the nature. In the years to come, their number should diminish drastically, thanks to the new measures, amongst which the obligation to microchip each dog, which becomes traceable and under the entire responsibility of its owner.
2. Stray dogs and cats, if not adopted, are not under the responsibility of a casual caring person. There is a campaign going on for months, allowing people to bring an adopted stray animal to a municipal vet or to the local Direction of Agricultural Development (Διεύθυνση Αγροτικής Ανάπτυξης) to let it microchipped and/or neutered. One pays only the cost of the microchip, nothing else.
A child learns to crawl before it can walk, after what, very quickly, it learns to run. Regarding pet animals, Greeks are crawling for the moment, but they will be walking and running very soon.