Hi Colleen, You're asking a "Universe" of questions, and if we were to answer them fully, we'd be writing a full guidebook here ourselves. If you can do a little wee bit of homework, you can learn a lot --- and be realistic in how much you can cover in 14 days.
Have you considered looking at some Guidebooks?? You don't have to buy them, you don't say where you're from, but Im guessing you are from the USA, and good libraries have tons of books to use free. If your local branch doesn't have them they can get them from central Loan. Or run over to Barnes & Noble and browse there for Free. To sort out what's possible, GREEK ISLAND HOPPING is Great for first-timers. It shows the ferry routes, and what you can hope to cover in 14 days (it's going out of print but libraries have it, also Amazon -- even used cheeep). Also ROUGH GUIDE to GREECE. I could give u some websites, but without knowing something, you can be misled by websites that sometimes are designed just to promote, not to inform.
Here's a MAP of Greece (click to enlarge) http://www.explorecrete.com/crete-maps/images/greece.gif You will see that some isles are waaay far from the others. You have proposed 8 destinations; you have time for 4, max. Look at those books, also look at this Ferry Map -- http://www.greeceathensaegeaninfo.com/ferry-info-greece/greek-islands-ferry-chart.htm
With such ambitious plans, you need to be efficient in Time-allotment. You will have to be in Athens at the last, to assure making your flight home. So why go there ALSO at the first?? When you land, leave as fast as do-able, for your first island, by ferry or plane. Which it will be, depends on your arrival time... so you need to share that, not just day. Also departure time: if you have a7 am flight out, that will affect your last-day plans.
On your sentence "we are more interested in unique cultural experiences (etc) is the next word "Then" or "than."? if it's "then," you need an itinerary that allows time for both. Finally, planning a trip requires figuring out the logistics FIRST --- and learning how much it takes to TRAVEL between one place an another will govern how much time you can STAY in each place. If it takes half a day or nearly all day to change islands, that drastically cuts down on your "stay" time.
Given your time limits, I would drop Crete (160 miles long!) and Hydra (not up to the other isles you list). Also, realize that Delphi is a 3.5 hour bus ride each way -- and the 1-day tours give you only about 90 minutes at the ruins and museum. Then the tour leader drags you off for lunch (which you pay for) and a souvenir shop/rug shop you don't want to see (but the bus folks get a kickback for taking you to) ... So if you want a memorable Delphi experience I think it requires going up on a noon intercity bus, seeing the museum before it closes at 7, seeing the ruins 8-10:30 in am, then taking a bus back to arrive about 5 pm. So... it's a day & half. Something to weigh when choosing your destinations.