Grombart: This game (or whatever it is) really looks interesting, but i have a few questions to which i can't find clear answers on the page:
Do i need to be online to play? Somewhere it says something about being DRM-free but somewhere else it says i need to authenticate with their servers at least once per installation.
There's authentication in the same sense as any other download service, in that you have to log in to get the thing in the first place. You get a launcher, and the first time it's run, you have to log in so it can download the game files. After that, it can be played offline. I'm pretty sure the game files can be copied between machines without problems.
Grombart: Is it easy to update the game? It says there are regular updates, so is there some kind of automatic updater or do i have to manually patch every time a new version is released?
Yes, the launcher also handles updates. You'll have to be logged in for that as well.
Grombart: Can I play this game in single player mode without having to set up a private server or so? I always read something about servers to play on.
Servers are just for multi player. For single player, you just pick a save slot to create a world in, and go.
Grombart: How stable is this Alpha version? Can i build up something without having to worry about constant crashes?
Single player is very stable. I've never seen a crash. I hear multi player can be pretty unreliable, though.
Grombart: Is there some kind of sandbox mode where you don't need to mine and craft stuff but have it all available from the start?
There's
creative mode, but it isn't supported any more, and there isn't a downloadable version. It's free though.
Edit: survival mode can be set to "peaceful" which removes the monsters and lets you concentrate on building. You'll still have to mine the stuff you need, but you won't have to worry about getting jumped by creepers.