1. Non-combat.  Of the Allied forces, only UK and Anzac can do that, though.  US can only take those islands if they are liberating them from Japanese control.
2.  If you mean Brazil, non-combat.  Other South American countries function exactly the same as other true neutrals.
3.  Combat.  You are attacking a pro-axis neutral with an Allied power.
4.  You can, but only when at war.  Russia has the additional restriction of only being at war on individual sides of the map.  That is, Russia can only attack Mongolia when at war with Japan, and it can only attack other (Atlantic side) neutrals when at war with Germany/Italy.
5.  If Spain/Portugal are still true neutrals, combat.
6.  You only acquire the troops of a true neutral if they have been turned into pro-neutrals (of your side) through the actions of a power on the other side.  As an example:
Germany decides to invade true-neutral Sweden and takes it over.  Now every other true neutral in the game is pro-Allied.  Now, on US’s turn, it can non-combat land units into Spain and take its forces as its own and the IPCs of the territory.