I have just had a similar problem with a recent guest.
main difference is this was two adults.
I would always suggest checking the room as soon as possiable after your guests depart.
a giveaway that they have stained your sheets is if they try and half strip the bed.
if you can get some stain remover on the sheets straight away then wash soon after you can get most stains out fairly easily.
as said before always take photos incase you cant get the stains out so you can raise the issue with airbnb support.
as for the mattress I have being lucky enough that no stains so far have gone through to the mattress.
I would definalty recommend investing in quality mattress and pillow protectors.
I have already had wetting of the bed, make up stains and coffee stains.
most guests are clean and respectful, its the few bad eggs that ruin it for everyone else.
It is our resonabilty as host to pre plan and prevent this issues wherever possiable