Is this much hair coming out after brushing normal?

Hair loss needs an in-person evaluation. I  recommend getting a formal evaluation with a hair loss expert to go over your condition and advise you on best treatment options and shampoo recommendations. There are great non-invasive options like prp/progesterone and/or hair transplantation. See an expert. Best, Dr. Emer

For humans a general rule usually holds true: Nobody knows their shedding patterns better than the patient himself or herself. If you suspect something is different, it likely is. Please see your physician for careful evaluation. 

Since your hair is longer it is more visible than someone with, say... a buzz cut.  You need a baseline to be able to tell.  Start actually collecting and counting the hairs for a week (just on your brush, pillow and drain) and then count them all and DIVIDE by 7 for an average.  You may just be going through a seasonal shed, you may have a high baseline amount of shedding.  The other way to check is the HairCHeck device which will show you a very accurate measurement of how your hair's MASS changes over time.  Good luck!

I can't tell the answer to that question as the average person losing 100-150 hairs per day. If you had a HAIRCHECK instrument check, it will tell quickly if you are losing hair. See below