Does intentionally inhaling incense affect prayer as it affects fasting?

Ruling on inhaling incense while fasting:

What is forbidden is inhaling incense that has a physical substance which reaches the internal cavity. If the smoke reaches the throat by the choice of the fasting person, then a make-up fast is obligatory. However, merely smelling the scent does not break the fast, and there is no harm in using perfume.

Is it permissible for a worshiper to smell incense and perfume?

There is no harm for a worshiper in smelling perfume or incense. It is a Sunnah to perfume mosques with incense, and there is no harm in placing the censer in front of the worshipers, because its embers are not considered a flame-producing fire resembling the temples of the Zoroastrians; rather, it serves the purpose of perfuming the mosque.