POISON
At the beginning of your turn, give this character a free action and deal 1 damage to each adjacent opposing character.

Question:
1) Does Poison damage stack on each other? Meaning If I have 4 characters with poison adjacent to an opposing character with toughness. Will the opposing character take 0 damage or will he take 4-1(toughness)=3damage?

You have to give each of your characters a free action to activate poison, so it will happen one at a time. This means a character with toughness will take 0 damage.

INVINCIBLE
Half of damage dealt to this char acter is ignored.

2)Would a character with Invincible receive 1 damage or 0 damage because of poison?

0. Invincible rounds up the amount of damage it ignores.