Thanks a lot for your feedback!
I'm happy to hear you like the new version so far!
Yeah, that's indeed intended, although islands sometimes tend to be a bit smaller than expected. They're supposed to be roughly 8000x8000 blocks in size, but if the game spawns too many lakes and bays, the resulting land mass is sometimes smaller (or a large island is suddenly divided into several smaller islands). It's definitely our intention to provide more control over that in the future (we want to stick to the island approach, but you would get more control over the island size, mountain ratio etc) 
Unfortunately deserts aren't implement yet, but they're on our to-do list
I guess they will be ready in the next couple of months^^
In MP, everyone spawns on the same island (at the same location)... probably most servers will use the spawn island as main island atm. We'll keep an eye on this to see if this will cause any problems in the future 
Yes, if you go to the crafting menu and double click on the row boat, you can craft a storage box that can be attached to the boat 
Once bigger vessels are implemented (e.g. sailing ships), you will also be able to place regular chests on them^^