If you apply by yourself:
The waiting time for getting a International passport is 30 days if you apply in your city (where you're registered) and 120 days if you apply from another Russian city.
Official source: https://www.gosuslugi.ru/pgu/service/10001970310_5.html#!_description
Just if you're going to funerals or if you need to be healed abroad urgently, a passport will be ready for you within 3 days.
It's cost 2000 rub (old type) or 3500 rub (new type) (for citizens over 14 years old) which is around 24 or 41 EUR (today)
But as @IMil mentioned, there are services which claim to get a passport done quicker.
offers it for 4-30 days, for extra 7000-25000 RUB (around 84-300EUR)
Scammers mostly targeting dating web-sites, therefore if the girl from a dating site asks for money it's very likely a scam, because it's a super popular scheme.
Normal Russian girls won't ever ask for money, only gold-diggers and scammers.
Very often you're actually talking to a Russian guy who is sending you a very nicely prepared love messages with sexy girl pictures :)
I wouldn't recommend anyone to look for Russian girls on dating web-sites, better on some interest related web-resources where their reputation is proved by a community.
Even Better would be to come to a small city in Russia (Not Moscow or St.Petersburg), look around there and choose one ;)
Though you better go for "English club" meetings or something like that, as not so many Russian girls in small cities speak English well. (You can find this kind of meetings and groups on vk.com or couchsurfing.com)
Remember there are Russians "earning" lots of money by fooling foreigners to send money for their tickets, passports and some medical operations for relatives and etc...
Don't support scammers by sending them your money.
In the 90's most Russians got scammed at least once or twice, everyone is aware of scammers, but still Russian scammers easily scam Russians again and again. Fooling western people is super easy (because you didn't experience getting scammed as often as Russians). It's good for the Western world that aren't so many Russian scammers speak English yet.
P.S.: I Love Russia, I'm Russian.