Well, well, I'm the resident Greek around here so...
As far as Greek airport security goes, you've got nothing to worry about, it's pretty relaxed compared to the UK, where they ask you to take your shoes off and so on lol.
When you go to Rhodes, don't forget to visit;
Elli Beach (or as I like to call it 'boobie beach', lots of topless women mostly swedish etc(i thought up that name when i was like 14)) That and the water's crystal clear. There's also a cool dive platform that is great fun to jump off. Just don't look down before you jump
Then there's the Old Town. As far as touristy gifts goes, don't buy anything in a rush, chances are another store will have the exact same thing cheaper just further down.
There's a scuba diving boat in the main harbour area so you could go out for a Padi Discover Scuba trip.
There are also small ferries that go out to Turkey for the day, as well as the island of Symi.
Other than that, have fun. Don't be surprised if you hear the word Malaka a lot. It's similar to the Brits and the word 'Mate' (stereotypical i know), except the word Malaka means Wanker. It can have a negative meaning, i.e shouting it at a bad driver, or a friend way ; 'come on re malaka, lets go for a beer'.
Other that, some top phrases depending on your age might be;
oraia vizia - nice t*ts
popo ena koloraki - damn what an ass
pou einai i toualeta - wheres the toilet
evcharisto - thank you
nai - yes
Hope I was helpful