Bekarim means im single. So couldn't we add on "bekarim değil"?
No - to negate an adjective, the person endings go on the "değil" and not on the adjective.
So "bekâr" + -im = bekârım, but "bekâr değil" + -im = bekâr değilim.
You must put " ım" but next to the last word
Interestingly there word "bekar" sounds very close to the Arabic word "بِكر" which means "virgin", can it be used with the same meaning in Turkish?
I'd say bekar is more closely translated to bachelor.