Time counters are usually found on cards with suspend and vanishing, but may be found on other cards as well. Notably, Sagas use lore counters to track their progress, not time counters. You can't move a Saga's chapters forward and backward this way.

If the target of Killer is illegal as the spell tries to resolve, it won't deal damage to any creatures.

To time travel, look at each permanent you control with a time counter on it and each suspended card you own in exile with a time counter on it. For each of them, you choose whether you want to put a time counter on that card or permanent, remove a time counter from it, or do neither. Then those changes all happen simultaneously.