The starship has stats like damage and so on. I know that the class (C, B, A and S) somehow increase those values? But i have now exact idea on how this is calculated.

Also another question: I have a B starship and i never run in an enemy that could even kill me half. Is there any other reason why we should upgrade a ship to get better, if there are no enemys that are strong enough to kill us?

Older versions of the game showed the stat bonuses as a percentage, so it was easy to tell how much better (or wrose) a particular ship was.

HG changed the display to a numerical value in Beyond and it makes it far more difficult. Supposedly patch 2.24 is going to bring back the ability to see the percentages again so we'll be able to compare much more easily. The 'prestige' of having S class aside, if you want to max out a particular attribute. For example, if you want maximum jump range, then you'll want an S class explorer. Maximum shields? S class hauler. Maximum damage? S class Fighter, although as you noted, there's not much that's a threat even if you're flying a bottom of the barrel C class shuttle.

Slots could be another reason as well. Lower class ships tend to not have the maximum slot counts for their tier.

In near future stats may not always be better, at least with ship type. Notes for Experimental include:

•The upper bounds for some starship stats has been increased on haulers, fighters and exploration starships, so that exotic ships are no longer guaranteed to the best at each specialisation.

I've seen that my damage also increases when i build things like weapons in my ship, is that correct? So if i have a S class Fighter and i build a new weapon, it increases the damage more then if i do that on a e.g. B class hauler.

Yes, fighters get a large bonus to weapon damage, with higher classes getting larger bonses. Depending on the class, Haulers get no bonus (C class) to moderate bonus (S class).

what do the yellow bars next to the white ones mean?

That's the bonus. The white is the base stat and the yellow indicates the extra you get from all bonuses to that stat combined (upgrade modules, and the ship type bonus).

@TerriblePurpose
ah i see, thanks for explaining!