As for nose drops, if they reach the back of the throat and they can be tasted, then it invalidates the fast. This is because the prophet encouraged the snuffing of water unless one is fasting.
Laqit ibn Saburah narrated that the Prophet (peace be upon him) said: Snuff up water freely unless you are fasting. [Sunan of Abu-Dawood Hadith 2360]
As for ear drops, they are permissible because they are not openings to the stomach but it is better to be cautious and refrain from using them during the fasting period.
Regarding eye drops, they do not break the fast because they are not part of the body cavity.
In summary, eye drops and ear drops do not break the fast, although there may be some scholarly disagreements on this issue. If, however they can be tasted or provide nourishment, then they are not permitted.