State-based actions don't apply to you or other permanents you control. (You don't lose the game due to having 0 or less life or drawing from an empty library. Your creatures aren't destroyed due to damage or
deathtouchDeathtouch is a static ability.
A creature with toughness greater than 0 that’s been dealt damage by a source with deathtouch since the last time state-based actions were checked is destroyed as a state-based action. See rule 704.
Any nonzero amount of combat damage assigned to a creature by a source with deathtouch is considered to be lethal damage for the purposes of determining if excess damage is being dealt.
The deathtouch rules function no matter what zone an object with deathtouch deals damage from.
If an object is no longer in the zone it’s expected to be in as an effect causes it to deal damage, its last known information is used to determine whether it had deathtouch.
Multiple instances of deathtouch on the same object are redundant. (CR 702.2) and aren't put into a graveyard due to having 0 or less toughness. Your planeswalkers aren't put into a graveyard if they have 0 loyalty. You don't put a legendary permanent into a graveyard if you control two with the same name.
CountersTo counter a spell or ability is to cancel it: remove it from the stack without resolving it. A counter on an object or player is instead a marker that changes characteristics or interacts with rules or abilities; for example, a +1/+1 counter modifies a creature’s power and toughness. (CR 701.6; 122.1) aren't removed from your permanents due to game rules. Permanents you control attached or combined illegally remain on the battlefield. For complete rules and regulations, see rule 704.)