So, I just got back from Ukraine, where I met a women that I really like (and apparently the other way around too). I am thinking about inviting her for about a week to Western EU, but I'm wondering if she will get a visa and how it works. She has 2 kids, but would come over alone and she does not live in Kiev, where the ambassy is. Can she arrange everything through a travel agency (passport, visa, flights, etc...) ?
There are only one or two people that can make s successful visa application, one of them is her and the other, in a sponsorship capacity, is you.
If she doesn't have a passport then she's not going to have anything to put a visa in, a passport application can be quite lengthy in Ukraine thus that should be your/her first step.
Flights, you can book them online or via your local agency, it's simpler online.