Full scale war in South America during WW2?

  Those are options.  Might be more likely Argentina v Chile with probably Bolivia and Peru also pitching in against Chile and then say some other powers come in on Chile's side for whatever reason.

  A few years back on the AH site there was a fascinating TL which historically involved Peruvian pressure on Ecuador resulting in the latter conceding quite a lot of territory.  However in this TL Ecador goes to war and produces a skilled and motivating general who gets nearly to the gates of Lima before he has to withdraw.  Things escalate from there with a lot of Latin America being drawn in and finally the US.  Unfortunately because Ecuador had had some pre-war support from Germany and a degree of identity of the regime with fascism the allies come in against Ecador and its allies.  [Plus also I think the powers of the opposing coalition were too economically important compared to their opponents].  This was about the time I left AH so can't remember more.

  In answer to the 1st question I would suggest splat!  Apart from the fact its got an awful lot of British influence and interests at the time so any dictator who suggested it might well end up quickly replaced Britain has too much global power at this point for the Argentinians to stand any chance of holding it even if they win it. 

  Possibly if your suggesting some impromptu alliance when the Graf Spree turns up?  They might think they have a chance but the RN had a lot of ships on the way and it would also mean war with France while the US wouldn't be happy with Argentina inviting Hitler into the western hemisphere.