You pay the costs for an exiled card if you cast it. You may pay any alternative costs the card has rather than the card's mana cost.

Damage dealt by a creature with toxic grants the same number of counters regardless of how much damage is dealt. Notably, if a replacement effect modifies the damage in some way (such as that of Gratuitous Violence), the number of counters given remains unchanged.

If you leave the game, the cards remain exiled face down indefinitely. No player may look at them.

Ixhel doesn't change when you can cast an exiled card. For example, if you exile a creature card without flash, you can cast it only during your main phase when the stack is empty.

Conversely, replacement effects that apply to the number of counters put on a player can modify the counters placed this way. For example, Vorinclex, Monstrous Raider's last two abilities can apply to counters placed this way.

You may look at and cast the exiled cards (and spend mana as though it were mana of any color to do so) even if Ixhel leaves the battlefield. If another player gains control of Ixhel, that player can't look at or cast the cards, and you still can.

If a creature with toxic deals combat damage to a creature or planeswalker, or if it deals noncombat damage, toxic has no effect and no player gets poison counters.

A player with ten or more poison counters loses the game. This is a state-based action and doesn't use the stack. In other words, it happens immediately and players can't respond to it, just like a player losing the game due to having 0 or less life.

Casting an exiled card causes it to leave exile. You can't cast it multiple times.

Any other effects of that damage, such as life gain from lifelink, still apply.

Toxic doesn't change the amount of combat damage a creature deals. For example, if a 2/2 creature with toxic 1 deals combat damage to a player, that creature will deal 2 damage. The results of that damage are the player loses 2 life and gets a poison counter.

Multiple instances of toxic are cumulative. For example, if a creature has toxic 2 and gains toxic 1 due to another effect, combat damage that creature deals to a player will cause that player to get 3 poison counters.