Can a planeswalker ability be activated in response to another spell or ability?
No, a player can't activate loyalty abilities during his upkeep nor in response to spells or abilities. Loyalty abilities can be activated at "sorcery speed", only during a player's main phase. The specific rule from the Comprehensive rules is:


  606.3. A player may activate a loyalty ability of a permanent they control any time they have priority and the stack is empty during a main phase of their turn, but only if no player has previously activated a loyalty ability of that permanent that turn.