What happens if I draw an Invasion card and the Giant Amoebas end up attacking the player to my right, who rolls the dice for the Alien?    

If your opponent chooses to defend against the Aliens, then you (as the player to the left of the player being attacked) would roll the eight sided dice for the Aliens.

Do the Giant Amoebas ever move out of the spaces they have invaded into?    

No, they do not. They will defend if they are attacked, but they do not invade out of spaces they control.

If Giant Amoebas invade an opponen't space next to me, can I let him retreat his units out of that territory through one of my territories?    

No, you cannot.

Can we use Command cards against the Giant Amoebas?    

No, you cannot. They are immune to nuclear weapons and they appear unexepectedly so cards such as Stealth MODS cannot be used to defend their invasion.

If a Wartime Inflation is in effect in round 5 do you still have to pay an extra 1 for every Colony Influence? (Sent to: This e-mail address is being protected from spam bots, you need JavaScript enabled to view it )    

No, Colony Influences are not considered to be played on turn 5, so you do not have to pay for them.

When playing Heroic Resistance Leader, do the two units come from the same territory and is the new commander placed in that territory?    

Yes, the two units are being replaced (This is an official WOTC FAQ answer).

When amoebas are attacked, the defender left has to role the dice for the amoebas. Can he decide to role one defending die even when there are two or three amoebas present?    

The amoebas always defend to the best of their ability, and with as many of them as you are able to fight with. You have to roll as many dice as you can for their defense (This is an official WOTC FAQ answer).

If Wartime inflation had been played will the humanitarians faction have to pay 1 energy for their free card or are they unaffected?    

The humanitarians get their card still for free. They are not required to pay '0 energy' for it in the wording, so they still get it just the same for free since their is no actual cost associated with it (This is an official WOTC FAQ answer).