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1) Water melts ice, right? Maybe even the cold water was too hot for them?
2) Apart from the guy having visions like many have suggested (knowing the dragons were coming), I have no idea. Maybe he had a limited supply.
3) About the raven, we already know they can fly pretty much anywhere. It must have taken it days to reach Dragonstone. You can see Jon Snow and co. are already almost freezing to death when Dany shows up. It would take her a lot less time flying on the dragon then it would for the raven to reach her.
4) I don't remember Drogon sitting right in front of him, but that's a good question.
5) Yeah, that was a very hollywoodesque moment. I liked that Jon survived but the "savior showing up at the last second out of nowhere" thing seems beneath GOT.
6) Could it be possible that they can manipulate ice's structure, turning it into anything? I seem to remember those chains were made of ice. Or, again, they brought them along since they knew the dragons were coming because the big bad guy has visions.

I liked the episode but I agree that since they ran out of source material it's getting a lot more cliché, and the plot armor thing. People keep getting saved at the very last moment (Jamie, Jon...). That's all very nice but in true GOT fashion they would have been history, This isn't some typical action movie. Anyway, I'm not a GOT expert so hopefully other people have better answers.