I am 25, female, non-smoker and the corners of my lips are becoming dark. What should I do?

Please start vitamin B-complex, make sure that your toothpaste is not coming in contact with your mouth corners and perioral skin, use a good quality sunblock and also some cream containing vitamin C.

I am going to lose all my hair at the rate at which it is falling. I heard hair mayonnaise helps in hairfall reduction. Is it worth a shot?

Hair mayonnaise can be used as a protein rich hydrating mask for your hair, it can make them softer whereas your hairfall needs a proper evaluation.

What should I apply on my face after a face wax?

A good hydrating moisturiser.

Is a facial oil at night sufficient or should I be adding more products to my nighttime routine?

Other products can be added depending upon your skin type and concerns.

I want to use a derma roller for my scalp. Please advice what kind of roller to invest in?

For hair you would need specific hair rollers. They are a bit different from dermaroller used for face. To start with, 0.25mm-0.5 mm is recommended.