Women can join the Russian military. Most often they join in warrant officer positions (technical or personnel related roles), although there are some women officers as well (mostly in the medical corps, but some in communications as well, and recently they started accepting women pilot candidates in air force academies). Both of these types of roles would require you to qualify for and then complete military academies first; and it goes w/o saying that your Russian language skills will have to be pretty good too.
You will certainly be serving with men together in some of these positions but you will likely have your own accomodation and so on (warrant officers and officers don't sleep in barracks with a bunch of 18-y/o conscripts anyway). You should be perfectly safe - more than likely you will be serving mostly with men but those a little older who often have families and so on... even when it comes to conscripts though there is no culture of rape or sexual molestation of women or any of that sort of degeneracy in the Russian military.
Your language skills might make you quite interesting/valuable for the Russian MoD; especially given that you are from the Middle East and speak 2 of its major languages.
Your shooting skills are rather irrelevant, Russia used women on the front-lines in combat in WW2 and even limited amounts in WW1 but these were measures undertaken at times of shortages of manpower and dire need. So if that's what you want to do then maybe go to the US Army or British Army instead where neo-liberal ideology dicatates and they're still carrying out all these social engineering experiments and will be happy to use you as a poster girl for the end of gender identity and what not.
But no matter what your position in the Russian armed forces you will still be trained to use firearms and some basic field skills anyway; don't think it will all be behind a desk in any case. Especially not for the medical and air force proffessions.
Only thing is that I really don't know about foreign women joining; I wouldn't say its unprecedented as often you have the wives of servicemen in various garrisons going into the military themselves, and surely some of these women must be citizens of ex-Soviet countries other than Russia.
Information on service for foreign citizens in the Russian military tends to be pretty contradictory. I'd advise you to continue working on your Russian, travel to Russia, get to know the country, and maybe then make some inquiries. If you're serious about it maybe I'll lend a hand.
You might be interested in this story BTW, about an Afghan girl currently studying at a Russian Interior Ministry (police) academy in Volgograd:
Of course that's a bit different though, as these academies take students sent by foreign governments for the purpose of those students to then go back and work in their own country's police or military forces, rather than Russia's own.