Ick,
I am by no means an expert (When it comes to our Visa process I am SERIOUSLY a novice) but you will find all the information you need at
www.immi.gov.auHere's what I understand (but please check everything yourself):
Effectively there are two visas you can apply for...A Spouse Visa if you marry before the visa application and a Prospective Marriage Visa (which is a fiance visa).
If you apply for the fiance Visa your fiance MUST enter Australia AND you must marry within 9 months of the visa being approved. I don't think there is a stipulation that the marriage must take place in Australia. She can come here after the visa approval and then leave whenever you want and follow up with the wedding later (but within the 9 months). You'll have to complete the Prospective marriage Visa process with documents confirming your marriage though.
Your absence from Australia might affect her permanent residency status though... From memory I think I read something about the Visa applicant needing to live in Australia for at least 6 months (in total) during the 2 year qualification period. Check that out... it'll be important.
After 2 years you need to prove the relationship is ongoing and genuine and then she gets permanent resident status (but not Citizenship yet).
When it comes to citizenship I'm pretty sure I just saw some recent changes on the Dept Immigration web site. It now requires 4 years NOT 2 for an immigrant to be granted citizenship. They also must sit a basic English and Cultural "compatibility" exam before they can become citizens. (They could be asked crazy questions like "What is a Fair Go" or other basic questions like, "What is the capital of Australia".
As for her traveling to, and living in other countries before becoming an Australian citizen you'll have to check with the relevant countries websites.
As I understand it an Australian resident (who is a citizen of Ukraine) can travel to NZ as freely as an Aussie but other countries are different. I'm not sure about Sing or UAE but as I understand it a Citizen of a FSU country who is resident in Oz would still need to go through the USA Visa process for short terms stays... Obviously her marriage, assets etc in Australia would be looked on more favourably than a single, sexy Russian wanting to visit her BF in the States.
Anyway... unfortunately there are very few decent Visa support groups or websites for us Aussies but the Immigration web site lays everything out pretty simply. When the time is right, if you want you can also phone Immi and ask questions... They won't give you tips and advice but they will answer your specific questions about the process.
Cheers,
Kuna