do all 4 players see the same assignments, will my eat 4 semlas assignment show for anyone, for people that need the bakers hat
Yes it should.
But to be honest idk.
Actually the assignments don’t seem to be controlled by avalanche any more. Some said that they now even work offline. So maybe they’re even random for everyone each week. 
As far as I know, assignments are just for the host, they are the only ones that get credit for doing them anyway. The other players, guests on the host’s map, can still collect loot and so on. But no credits, same as missions.
That is tricky, but the baker’s hat is an achievement, if I remember correctly. They are like the collectibles all over the map, you can still do them for yourself on someone else’s map. At least when I did them a few years ago, seems that is the way they worked.