So, I just finished the game on medium. I got a 100% completion on the items and therefore unlocked the golden guns.
 
I just started a hardcore game and were surprised by some things. Please enlighten me: 
 
First, I jumped directly to level 20. Is it supposed to do that? Does the level in hardcore depend on my progression on medium somehow?
 
Second, I got acces to the golden guns room straight away. Is that because I unlocked it on medium? Will the game really be that "hardcore" when I get to use tha fattest gun from the start?

Your level and the Golden guns carry over for your save, everything else is reset

Okay. But I also got the whole map with all the question marks.
 
The weird thing is that I never got to level 20 on medium. I only got to like level 13. Shouldn't it start on that level then?

I dunno my level didn't jump between difficulties..
 
But XP scales to the difficulties

" Okay. But I also got the whole map with all the question marks.  The weird thing is that I never got to level 20 on medium. I only got to like level 13. Shouldn't it start on that level then? "