Yes to all your questions.
When Germany activates Finland (3 icps), Hungary (3 icps), Bulgaria (4 icps) and Romania (6 icps) Germany adds these amounts (16 icps) to there income total. Also each one of these pro-axis neutrals collects the same amount for there own income.
The pro-axis minors can buy each turn and place in there territories only. Finland only in Capital.
I actually had different colors for all pro neutrals in game. With Pro-axis neutrals for thee above 4 with different color armies you can see what the Germans are buying and not getting confused if you make them all German looking pieces. Keeps the buyer honest or others can see the buy.
The buy most times in game per turn is Finland 1 Inf, Hungary 1 Inf, Bulgaria 1 Art, and Romania 1 Tank or sometimes 2 Inf.
Germany also likes to buy a Major factory in Romania to get a bunch of Inf for fodder quicker to the front or Mechs, Art for blitzing or a stack of tanks to run down to Leningrad or push into Stalingrad or a naval base in Romania and if Russia income allows them to go to war against Germany turn 4.