Can mircodermbrasion remove early signs of aging under eyes? and how many sessions are required?

Not used for this: I generally don't recommend microdermabrasion for this purpose. The sensitive skin of the eyelids is too delicate for the suction and the foreign particles driven against the skin can cause corneal abrasions. I would recommend other forms of exfoliation.

Micro dermabrasion: Depends on the signs of aging. Micro dermabrasion is good at smoothing fine wrinkles, though it does require multiple treatments for a noticeable effect and to maintain that effect. It will not treat deep wrinkles or the tear trough. Make sure the aesthetician is certified and preferably under the guidance of a board certified dermatologist or plastic surgeon.