Is it permissible to apply a honey mask to the face, knowing that some of it may enter the mouth and be tasted without being swallowed? And is that considered among the things that invalidate the fast?

There is no harm in using honey on the face to remove melasma and soften the skin, provided there is no extravagance. This is based on Allah's saying: (It is He who created for you all of that which is on the earth), and His saying (for you) encompasses general benefit unless there is evidence indicating prohibition. However, if honey enters the mouth and you taste it without swallowing, it does not invalidate the fast.