This is a picture of a particular dance form called Bharatanatyam prominent in the southern part of India. The dance is usually done with music in the background and utilizes facial expressions and body movements to show the meaning of the song. Dancers adorn jewels and exquisite costumes while giving performances. 
PICTURES OBTAINED FROM :-
http://www.dollsofindia.com/dollsofindiaimages/woven-bamboo-blinds/bharatnatyam-dancer-wall-hanging-HF82_l.jpg
Why is there a red stain at the bottom of her feet? Is this a depiction of menstruation? Fertility?
it is mehendi which they apply on hands and legs.
On second thought, is she crushing grapes to make wine?
Or berries to create a henna dye?
Since the picture is actually a painting of dancer, Its probably an artistic element incorporated by the artist most probably as a symbol of something like you said. However, I have never seen this in real life dancing though.
they crush henna leaves to make a paste which they apply on hands and leave for few minutes. when they remove it they have red designs on their hands.
This painting is beautiful. I mean look at the strong contrast set by the vibrant colors! Just one tiny question, when these dancers perform, do they distinguish their social classes by the way they dress or their make up/ jewelries? Also, were women allowed on stage back in the traditional time period?
Its usually always portrayed with color in paintings! There weren’t exactly any huge differences. However, different dancers usually had different techniques for costumes. Women were actually allowed to perform. During the reign of many Southern Kings, these dancers were often a form of entertainment. However, some others performed for deities/Gods.