This site is not just for code golf, but as you point out, the questions are heavily weighted towards code golf. This is the exact reason for the name change. Code golf was being emphasized too much, and people were a) not visiting the site because they thought it was only for code golf questions, and b) even if they did get here, only saw code golf questions and didn't participate. If the name of the site is actually harming the site, that absolutely needs to be looked at.
As for putting programming puzzles first, code golf is a subset of programming puzzles, so even listing code golf separately is a bit iffy for me personally, much less listing it first and putting even more emphasis on it.
So, I can't do anything for #1 right now, but #2 is exactly the reason for the name change.