What dermaroller size should I use for hair growth without scarring? If 1.5mm, how often should I dermaroll to avoid scarring?

I typically do not recommend using anything above a 0.5mm for at home rolling. Any amount over this should be done by a board certified physician. See an expert for anything above 0.5mm to ensure your safety and to prevent worsening of your concerns. Best, Dr. Emer. 

Hi,
That is a great question.  The answer depends on age, skin type, current health of skin, are you prone to scarring,  and what area of the body you are derma rolling.
But more importantly,  per the FDA, a micro needling device that is greater than the 0.5mm is a medical device that should be used by a trained medical professional only during procedures.  The 0.5mm is specifically used for home use and any greater length needles are designed to be used during medical procedures as you can cause more damage than good.
So, what area of the body are you using the dermaroller.  Face, scalp other areas.? I will get to scalp and hair growth last.
THE ONLY HOME USE INDICATION FOR DERMAROLLING  is to open up the skin barrier to increase delivery of a serum or medication to the lower layers of the skin, using a 0.5 mm derma roller works well and is all you need.  Once or twice a week with light to moderate pressure as tolerated ok for scalp or extremities.  If you are rolling face, keep the derma rolling to once a week. 
To specifically answer your concerns about stimulating hair growth and scalp you can treat to improve topical penetration and delivery, 0.5 mm works well and the needles should not be deep enough to injure the hair follicle which can cause shedding and damage to the follicle.  If you want to stimulate stem cells in the scalp to increase hair growth, then needling to a greater depth is important.  BUT, the last answer and use of greater depth needles is RESERVED for MEDICAL PROFESSIONALS.  
Bottom line is YES, any length greater than 0.5 mm runs greater risk of causing damage to skin when used in untrained hands.  Recommend you see a well trained medical professional in aesthetics, dermarolling and skin rejuvenation.
Hope that helps without ambiguity
Dr Joe