1) 梳头发 means “to comb one´s hair",it doesn't mean "to braid one´s hair or to add embellishment to it".
2)- He combs himself: 他自己梳头发。
Yes,it's correct,but we say 他给自己梳头发 more often.
- He combs his dog: 他梳头发他的狗 or 他给他的狗梳头发？
It's incorrect,because dog's hair is 毛 ,not 头发in Chinese.
-He brushes his dog : 他在给他的狗刷毛。
3)In Chinese,梳子is a comb or a human hair brush,刷子is a paint brush or an animal hair brush or other brush,like toothbrush.In a word,梳子is used for hunam hair in general.