If you decide to edit your zap while it's live, you need to be careful. The first thing to note is, as soon as you make a change, the zap will switch itself off. That means, until you switch it on, it won't trigger again. So remember to switch it back on when you've finished making changes.
Also keep in mind - when you switch off a zap any currently running tasks will stop.
If you want to replay them, you'll be able to do that from within the history tab. However if you've made significant changes to the zap - adding steps, removing them, or changing the app or action type associated with a step - then Zapier won't let you replay.
When you replay a zap it will start again from whatever step it stopped on.
This depends what type of delay step it is.
When a zap is switched off that contains a 'Delay for' or 'Delay after queue' step, in the History tab, it will look like there has been an error if you turn the Zap off in the middle of the delay. If you've not made significant changes to the zap, you'll be able to replay it from the delay step when the zap is switched on again.
If you edit or switch off a zap with a 'Delay until' step and turn it back on before the release time, it should continue to run as normal. If you turn it back on after the release time, it wont and you wont be able to replay it.
For this reason, it's best to avoid very long delay steps in your zap and instead break the zap into multiple ones, using webhooks or other methods to chain them together.