I was wondering if the craft beer has more nutritional values (vitamins and so on) than regular and cheap beer?
So... I guess it depends on what you're deeming nutritional value. Beer has 4 main ingredients:
The biggest mineral difference is going to come from the water source of the brewery. Following the exact same formula recipe/mashing instructions/yeast used/fermentation conditions (temperature, altitude, fermentation vessel)/time/etcetera... you can get very different flavor beers if the water source is different.
The next varying source of minerals would probably be in yeast. Unfortunately, I can only find evidence of all brewing yeast lumped together at the moment.
The interesting part in craft brewing, especially at the homebrew-mad-science level, becomes all of the additives that can be placed into beer. I once met a brewer that dry-hopped smoked salmon bones (right they aren't hops but the same technique) in their secondary fermentation (or clarifying stage) chamber!
These examples would be more "here is a random thing" that I found rather than being able to give you a definite answer as to "more nutrition" being provided than big-beer manufacturers.
It would depend on the craft beer. Regular cheap beer is not a good comparison as you don't typically get the same style of beer. Craft rules are not the same everywhere. Typical rules is water, hop, barley, and yeast. A non craft can use other ingredients but that same 4 is going to be the bulk. A craft tends to be denser so in the case it would have more nutrients.