I live in a condominium. Several neighbors rent out their apartments for days. At the AGM meetings they claim to have a tourist license. Is that possible?

In theory no.
only between 2001 and 2002, a few tourist licenses were granted in multi-family houses. There are very few of them.
Therefore, your neighbor may NOT have a tourist license because they do not currently grant licenses in multi-family homes.

How do I know if it’s true?
Ask your neighbor for his license number. Go to the Balearic Island Goverment and check if the license corresponds to your apartment block.

Can I know if there is any tourist license in my building?

Yes, the consellería of Tourism Balearic Island Goverment offers a register of the licenses that are in a given street.