There are some Free hot springs in Greece.
KTEL is the regionally decentralized monopoly of bus companies. It's relatively expensive compared to surrounding countries and every region has their own website (which would have been great in the 90s). Hitchhiking might be hard though you will be without any doubt be saved by foreigner, rich europeans on holidays or nice immigrants (usually from Africa or Indian continent) working.
Off season you can find good paying deals, but even in season a room can cost you 20-25€/night, if you are 2, it means the same price of a european hostel.
You can wildcamp almost everywhere, among olive tree fields, abandoned buildings,etc. Beaches are usually the best, take care of your belonging and tend to avoid cities, where you can easily find a host through Hospitality exchange and Spontaneous hospitality. There is only few greek islands where you can camp without any trobules. One of them is Agistri
Free hospexchange and spontaneous hospitality do work very well.
There's tahini in all supermarkets!
Dumpster diving may work in cities, especially after openstreet markets.
Table diving in touristic restaurant is a very doable option and generally greek hospitality is great, you will be offered food so many more times than you imagine, you can rely on that.
Free food is everywhere in the streets. You have plenty of figues, grapes, cactus pears (beware of small thorns!), blackberries, really a lot of fruits in the bushes/trees along the sidewalks (sometimes even in cities). Olives (and oil) are more difficult to eat since they need to be marinated and eating them raw is not really healthy nor tasty. They are not really cheap though definitely worth an investment..
Greece is part of the EU, works out great if you have cheap EU roaming. There's free wifi in most of bars and cafes, you can take something cheap or just ask for the password.
Greece belong to Mediterranean euro countries, which means, you have the same currency of other rich european countries but further lower average wages.
On the other hand it is one of the most favorite touristic destination for many rich or wealthy Europeans which makes it very very good for earning an income from the streets.
Touristic islands (e.g. Crete and Rhodes) or destinations on the mainland (Peloponnese as Meteora) could be further better option than big cities. Athens is kind of both, huge and also very touristic. Give it a try but don't stay too much, islands are much more beautiful and rentable!