First of all you don't know if it's a woman you are really dealing with. Could be a Boris using stolen model pics.
NEVER give money to someone without meeting them first in person and getting to know her very well. You need to get your butt on a plane to Ukraine and see if this person really exists and is REAL.
Don't take the lazy man's route "Send money and she will come". 99.99% of the time it's a SCAM.
janne66, it depends on how quickly she needs it. The cheapest price is around 400uah, the highest - around 1000uah.
But listen to TomZ - never gave them money before you met them in person.
And by in person i don't mean at skype!
"I checked with Swedish Embassy in Kiev and cost for Visa is 35 Euro for Ukrainian application for Visa to Sweden."
Yeah, if she is going to apply in Kiev it costs 35 euro, if another city then add 22,3 euro for VFS Global service.
As to passport... In summer 2014 I urgently needed new passport (cause I got denial in my old one),and it costed about 1000 UAH (as Moyarishka said).Maybe, a bit more now.
I think it was ready in three days cause in 10 days I got it with a Schengen visa.