Hello. Thank you for this opportunity to answer your questions.
Can my wife apply for Green card renewal from abroad or does she have to reside in the USA to do so?
She have to reside in the USA to pply for Green card renewal. As a U.S. Resident, your wife is expected to be living in the U.S., and only visiting abroad on a temporary basis. If She leaves the United States for extended periods, or cannot show her intent to live permanently in the U.S., she may lose her permanent resident status.
When and under what circumstances can my wife apply for USA citizenship. Which is the best alternative for her; to renew her Green card or to apply for US citizenship?
Applying for Citizenship is the best alternative for your wife. One of the conditions is to be married and living with you for last 3 years inside of the United States.
To apply for naturalization, she will need to file Form N-400, Application for Naturalization.
Click THIS LINK to find a general description of the application process.
Positive rating is very important for the experts. That is how we receive compensation.