Khums is not obligatory on you if you have no savings at all after receiving your annual income and spending in your lawful usual expenses. If you have any savings no matter how much, then Khums is obligatory on that savings once per year. After paying the Khums from any amount, the remaining amount is called Mukhammas (Khums paid) and this Mukhammas amount is exempted from Khums in the coming years as far as it remains with you.
It is very simple and easy to calculate Khums. It is just to calculate how much you have remaining cash in hand or bank or with people, and property except your residence, and remaining unused items. You calculate the total and take 20% which is the Khums.
A woman, single or married, is independent in her takaleef and obligations towards Allah ta'ala, even in financial matters.
A wife is not obliged to financially contribute to household expenditures, however she is able to do so out of her kind generosity and good-will. She is able to count that as her common expenses.
As for long-term loans, and her contributing to getting it paid of, it will not exempt her from khums should she have anything entitled for khums on her khums day.
This question is very broad, and I would firstly recommend that you do some reading on the background of Khums and its rulings.
A very brief reply to your two questions:
1. What items is khums compulsory on: (1) savings at the end of your khums year, and (2) items that you own but are new and have not been used all the way until the arriving of your khums day.
2. How should it be distributed: To be given to the office of your Marja' Taqleed, or his shar'i representative (wakil).
There are much more details, and as this is a fiqhi issue, you will need to refer to the fatwas of your Marja' Taqleed. I would recommend you go through this link, and familairise yourself with the topic:
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