Is it permissible to demolish a building that violates licensing regulations and was built on public property, after two of its floors have been converted into a mosque? And is it permissible to demolish the third upper floor of the same building, which is not used as a mosque?

It is not permissible for a mosque to be built on usurped land, and prayer in it is forbidden without dispute. Some scholars have even declared such prayers invalid. The method of construction by the company, as you described, indicates that they usurped the land. Therefore, demolishing the mentioned mosque is not merely permissible; it is obligatory. Prayer therein is not permissible, and there is no difference between the upper floors and other parts. This is unless all the owners have given their permission for its construction, and their permission is considered valid only if all of them are adult and sound of judgment. Ascertaining the opinion of all of them is extremely difficult. Consequently, demolition is obligatory in all circumstances.