The "total toxic value" of a creature is usually just the number after the word toxic on that creature. However, if a creature has gained multiple instances of toxic, the total toxic value of that creature is the sum of those numbers. For example, if a creature that has toxic 2 later gains toxic 1 due to an effect, it has both toxic 1 and toxic 2, and its total toxic value is 3.

The creature isn't chosen until the corrupted ability resolves. Notably, this means you may respond to that ability by giving a creature toxic (or more toxic) in order to draw more cards. (Of course, your opponents can also respond to try and stop you, but interaction is fun.)

You may choose any creature you control, including one that doesn't have toxic, if you don't want to draw cards. If you don't control any creatures, you won't draw any cards.

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.

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.

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

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.

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.

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.

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.