Can you play an instant in response to a planeswalker?

Since the active player gets priority after the planeswalker resolves, there is no time you can play an instant before they activate one of the loyalty abilites, unless they start the stack somewhere else with another instant or sorcery.

Does a planeswalker ability go on the stack?

Planeswalker abilities use the stack, and as a result they can be responded to, yes. The scenario you described works, and if the Lightning Bolt kills the guide, Elspeth’s ability will fizzle. (However, remember that adding or removing counters for planeswalker abilities is part of the COST, not part of the resolution.

Do instants go on the stack?

Instants, Activated Abilities both go on the stack. The stack gives players the opportunity to respond to spells/abilities before they resolve. The stack is a First In Last Out (FILO) zone, where spells and abilities exist until they resolve or are countered.

Can planeswalker abilities be interrupted?

No. There is a difference between an ability activating and it resolving. Activating the ability adds it to the stack, where triggers and instants and such are added as responses. The stack then resolves in reverse order.

Can you only use one planeswalker ability per turn?

Each planeswalker can only activate one of their abilities once per turn and only on your turn. It can only be used at a time a sorcery can be used.

What is the planeswalker rule?

All planeswalkers have supertype “legendary” and are subject to the “legend rule”. Planeswalkers with the same subtypes can exist under your control as long as they are not of the same name. Each of your attacking creatures can attack your opponent or a planeswalker that the player controls.

Can you remove all loyalty counters from a planeswalker?

You can add and remove loyalty counters from Planeswalkers by activating the loyalty abilities listed on the card.