Help me, pics inside

Yep.. and yep.
You need a 1/8 chain to fit that cog..

yep

Headset - can't really diagnose, but generally if it was OK, but now is loose, a spacer is required. Is the 'stack height' of the new stem less than the old one?
(stack height is the vertical height of steerer which the stem covers.)

The only other thing is to check your technique for doing up the headset. Sorry if this sounds patronising but are you loosening the stem before you do up the star bolt?