Do tears, application of lotion or balms nullify the fast? Is it permissible to eat pain killers before the fajr athaan is called out? Also, can a pregnant woman fast if she is healthy and the fast will not affect her baby?

Tears, balms and lotions do not affect your fast. Yes, it is permissible to eat pain killers before the commencement of your fast.

It is okay for the pregnant woman to fast. However, if the doctors say that it will harm the baby due to her own weakness, then she shouldn't fast.