I am a nanny so hopefully that’s helpful.
What is her annual salary based on? (How many hours per week have you agreed?)
Either way, ideally you should be able to calculate her hourly rate and use it as a base for all those scenarios.
1- Sick days. I assume she has a certain amount of paid sick days, so unless she goes overboard, she should be paid for them at her normal rate.
2- If you are late and go above the agreed schedule and her agreed daily hours, then yes you should pay her extra.
3- If you are gone for 24 hours, and she accepts to take on a 24 hours then you do need to pay her, her hourly rate x 24 at a minimum (the average amount for a 24 hour stint usually start at £300 per 24 hours worked and that usually includes a 4 hours break so if there is no break it should probably be more).
4- For holidays, if you take her with you then you are responsible for all of her transportation, accommodation and food, and yes for her salary also, which will either be the same (if it’s the same amount of hours just in a different place and the trip is optional) or more (if it’s more hours and if the trip isn’t optional she might ask for an extra fee for being made to be away from home for X days). If she works less than her normal week, she should still be paid her normal salary. If the trip is optional and she chose not to come then you should still pay her since it’s your choice to go on holidays (you can probably agree with her for it to be part of her holidays.)
In other words, you shouldn’t ever really pay less than her base pay and should pay more if you ask for more than what was initially agreed.