I got off the ship, and I can't do anything on the planet.
I don't quite understand what to do at the beginning.
My platform was destroyed, and I can't bring anything back. What should I do?

There is a very small chance of getting the right material.
I've been on the website for over 2 hours and still haven't been able to do anything.

Can I make the first and second materials mineable by hand? With mekhaskal and so on, not with scrap?

You can't play without steel, but it's unclear how to obtain it :(

It's not that simple as to start at Nauvis, but I'd recommend to gather some scrap. The first achievement can get hard but then things get rolling.
If possible, try to build a new ship in order to get some supplies from Nauvis. :-)

You shouldn't be having any problems landing on Carna if it was installed normally. If it was installed using an external pack (not a modpack that uses Carna as a dependency, but an independent repackage that puts everything into its own mod), you're going to experience problems. Make sure Carna mod is loaded on your game. If it is not, the mod will not work correctly.

As far as getting materials go, it is very hard to start from scratch on Carna. While it might be possible, it is not recommended. You're expected to be able to ship in resources. I am looking into making a Carna start though, but for now just import materials you might need.