Does Deathtouch kill indestructible?
Deathtouch destroys creatures by inflicting one point of damage, Planeswalkers are not creatures so they are not affected by deathtouch.
Regeneration can replace this event. 704.5h If a creature has toughness greater than 0, and it’s been dealt damage by a source with deathtouch since the last time state-based actions were checked, that creature is destroyed. Regeneration can replace this event.
There’s nothing in the rules about deathtouch cancelling out. They might be confused by “702.2f. Multiple instances of deathtouch on the same object are redundant.”.
Can Deathtouch kill a player?
Yes, indestructible creatures can be killed by reducing their toughness to 0 or less. As a sidenote, Tragic Slip does not give counters (but still it works).
Does desthtouch defeat indestructible? No, deathtouch causes “lethal damage” to creatures, indestructible creatures cannot be killed by “lethal damage”. 702.2a Deathtouch is a static ability.