@Patrik14 It all depends on the situation. If a guest damages your space to the extent that it cannot be reasonably be suitable for the next guest, I would advise you to contact Airbnb as this would likely be covered under Airbnb's Extenuating Circumstance policy.
Second, be sure to file a claim for damage through Airbnb's Resolution Center. For best results include photos of the damage, receipts or estimates for repair and any other documentation that would support the amount you are claiming.
To answer your specific questions:
1. If the guest needs to stay at another listing, their original payment will either be refunded or transferred as payment for the new booking. You will not be compensated for this reservation.
2. If the damage can be repaired, then you will need to file a claim for damages within 14 days or before the next guest checks in.
3. Yes, if the guest needs to book another space, you will not be paid.
4. No, if the damage was such that your space becomes unsuitable for the next guest you will not be penalized.
5. Here are some links that will give you more information:
https://www.airbnb.com/help/article/264/what-do-i-do-if-my-guest-breaks-something-in-my-place
https://www.airbnb.com/help/article/1320/what-is-airbnb-s-extenuating-circumstances-policy
https://www.airbnb.com/help/article/170/what-happens-if-my-host-cancels-my-reservation
If you encounter a situation that you describe here and need to cancel a reservation it is always best to discuss your specific situation with Airbnb.
I hope this helps!