The words for "boyfriend" and "male friend" - 男朋友，男性朋友，男的朋友
男朋友 mean both "boyfriend" and "male friend". Can 男性朋友 also mean "boyfriend" as well as "male friend"?


No, "男朋友" means 'boyfriend' exclusively. For both men and women. 

A woman would refer to her male friends as "男性朋友" or "朋友"

A man would refer to his female friends as "女性朋友" or "朋友"

Most of the time men and women just use the unisex term  "朋友" 


  Are 男性朋友 and 男的朋友 the synonym?


Yes


  If you have multiple "boyfriends" or "male friends", how do you express?


If you have multiple "boyfriends", they are all your "男朋友"

If you have multiple "male friends", they are all your "男性朋友" or "朋友"


  If a man uses "男朋友", does this mean he is a gay? Or does this always mean "male friend"? (and is there any other word to express "boyfriend for gay"?


If a man calls someone "男朋友", that means he is his 'same sex partner', and yes, they are gay.


  Are all the above the same in the case of 女朋友/女性朋友?


No,  women sometimes call their female friends "女朋友",  but usually just "朋友" ; Men never call their male friends "男朋友"

Women do not call their female friends as "女性朋友"

Men do not call their male friends "男朋友" or "男性朋友" , they just call them "朋友" 

In summary


Men and women usually call their friends "朋友". 
"男朋友" to a man (in a gay relationship) or a woman, means "boyfriend"
"女朋友" to a man, can only mean "girlfriend"
"女朋友" for a woman, can mean "girlfriend" (in a lesbian relationship) or "female friend" (in joking manner)