1. Is it no longer possible/relevant to annex countries? (since hoi2).
Faction members have a extremely high chance of going into exile if you use the conquer wargoal on them.
2. What do war goals mean (or rather do) when you dow a country?
That's covered in the manual.
4. If you attack from an allied province, do you get the conquered province or does the ally?
The province goes to the owner of the adjacent supply network.
5. As Germany, why does danzig have partisan activity - isnt it meant to be a core?
That's because occupation policies don't differentiate between cores and non cores. If you want the cores, you have to stall the fall of poland long enough (a month) to add another wargoal.
6. Playing as majors, do you need to do something to get your allies to do stuff? I'm playing as Germany, 1941, and Italy has not done anything in Africa or anywhere else?
You need to call them to war because Danzig or war only started a limited war. You can also give them allied objectives on the bottom of the province tab.