It means please as in please do x or please don't do that. It has a slightly admonitory tone (I was told by a Kiswahili scholar) and is often used on official signs. For example 'Nenda polepole tafadhali' (Please drive slowly).
yes, and it's actully feminine only in arabic masculine is tafadhal .. it can also be said if she said "can i ask you something?" -sure, tafadhali .. in arabic .. i'm not sure if it works in swahili too.
Tafadhali is used seldomly because of the (above) mentioned admonitory tone.
The polite form still is the bantu-based "Naomba." (short for - probably original origin - "Ninakuomba." I ask (from) you. The long form no longer or rarely is used.)
Ninakuomba is a different tense than naomba. Naomba means "I ask," (or "I pray"), while Ninakuomba means "I am asking you." (As in, the activity in which I am currently engaged is the activity of making a request of you.)