Hello 140
You know what they say about Med mooring.....practice practice practice... and try avoid doing it in a cross wind with a big ass tennis court cat !!
Quite honestly you will likely be amongst the most unpopular yachts in the harbour with your chartered cat... you take up too much room for the small harbours and will eventually loose control, of the thing when coming in to med moor and wipe out someones pushpit. Aside from that they really do not sail that well here and you will find that you will burn alot of fuel getting to your next port in a hurry so that you can find somewhere to park the thing so the ladies can go shore...
to answer the question on fuel.. diesel is currently 1.35euro at the pump but add another 20% when the broker sells it to you at check in time on the return... after all he has to make the phone call to get the truck to the yacht and fill you up!!
As for the Meltemi you should be safe in June at least from any strong winds... In the Cyclades in JUne it can be a mixed bag the last of the southerlys in the begining of the month and quite often no wind in the middle of the month with increasing trends to the north in the end of the month... the Meltemi proper really does not start until July....

and you DO NOT WANT TO BE IN A CAT when it blows or get caught out it in in one...
Last summer we had 2 cats flip one down by Milos a 'lagoon 38' and the second was just south of Ikiara, and older Nautich 42.... both as the result of bad handling and stupidity in big seas and big winds..
Avoid the marina at thira, 1. its still not finished. 2. there is are reef in fron of it and local knowledge is required to get in . 3. there are breaking seas with any kind of north wind . 4. its about 40 minutes outside of town with a taxi and of course there is no bus etc to get you there.. basically a waste of time building the thing where they did !!
and good luck anchoring in the caldera... how much chain do you have ? if you are lucky you may hit bottom in some places at 0ne to one, if you have 100 meters chain... but most cats only have 60-80 meters .. wieght you know they do not like all that weight up front...sinks the bows in a sea way !
as for you questions.....
1. it is illegal to build fires on beaches in Greece... we have enough trouble with fires on the mainland with out happy sailors building fires on beaches and burning down our islands
2. No snorkel gear... no BBQ on board.... what was that term 'BARE BOAT'.. pretty much sums it up huh!
3. Provisioning now thats a whole lot of fun when you have no idea where to go or what to buy... all ports have some sort of grocery store/supermarket, prices etc will reflect where you go and what island you are on... ie:- most expensive ...Mykonos, Santorini, Ios..
more resonable Serifos, Siphonos.... Delos is a national park and there is no overnight anchorage allowed. and Naxos is a beautiful island with excellent harbor facilities and even an American style marina where you can tie alongside... yeh no med moor!!
One final piece of advice read your charter contract WELL as 90% of charter companies prohibit yachts from going to Santorini . If you go and get damaged as a result or someone sees you and calls the company... well as they say... your "goose is cooked" and say goodbye to any security deposit...
These are not the BVI's nor the Carribean Islands, as a first timer I would have recommended taking an expereinced captain with you or better still contact one of the private 'Captained yacht charter companies' and use there services first time off... when you know the ropes come back and do it your self.... I fear you are in for a very stressful sailing vacation... good luck though..