What is the ruling on the transparent liquid drops that come out of a woman after or before urination: Is it considered urinary incontinence that necessitates ablution for every prayer, or normal discharge that does not necessitate that?

You did well to ignore the whispers. It appears that the mentioned discharge is from the normal vaginal moisture, which is pure and does not necessitate istinja' (washing the private parts), but it does nullify wudu' (ablution). If you are afflicted with an incontinence of this moisture, then perform wudu' after the time for prayer begins, and pray as much as you wish until that time expires.