Am I doing something wrong when the hairs break on my bow? Am I bowing too hard? I seem to break a couple most every time I play.

It could be that the bow hair is old, or of poor quality, or both.
I doubt that your bowing is too heavy.
Depending on hours of play bows need to be rehaired every year, or as frequently as every 3 months.
Bow hair will get brittle with age even if it's never used.

I notice that when I apply rosin to my boe that the cake will stick to a certain spot on the hair and sometimes it will break the hair. I have a $200.00 Brazilwood bow, could it just be that the cheap price of the bow is due really bad hair.

P.S. I have only had the bow for 3 months now, but who knows how long it's been in the store for.