I was wondering how far Beleriand extended during the First Age. Did it go up to the Misty mountains or retain itself to the Ered Luinand westwards? I thought that when Aule buried the Dwarves they were buried asleep in what later becomes known as Dwarrowdelf asnd I thought this was in Beleriand.
I don't know about where Aule put the dwarves to sleep, though Khazad-Dum is very likely to be the or one of the places, but Beleriand only extended from the great sea to the Ered Luin west to east and Thangorrodrim in the north down to that big scary forest in the south of which I can't remember the name. Dwarrowdelf is thus not in Beleriand.
it isn't likely, it is a fact that it was Khazad-Dum. Dwarrowdelf was simply the name in the Common Speech for the city mansions in Khazad-dum. Its meaning is "dwarf-delving".
Actually, "Beleriand" did not extend to the Ered Luin; the eastern border was the river Gelion. Nor did it reach Thangorodrim. The northern borders were the Ered Gorgoroth and the Ered Wethrin. The highlands north of that were not part of Beleriand, and the land between Gelion and the Blue Mountains was called Ossiriand.
As for where Aulë laid the Seven Fathers to sleep, none of them were in Beleriand. It's said that two (fathers of the Firebeards and Broadbeams) awoke beneath Mt. Dolmed in the Ered Luin, but that was as close to Beleriand as any of them were. They were said to have founded Nogrod and Belegost. Durin I the Deathless supposedly awoke beneath Mt. Gundabad in the northern regions of the Misty Mountains as well and then travelled to Khazad-dûm, but that's nowhere near Beleriand. (note: I'm going by memory here though, so some things -might- be off)