Γεια σου Ιάκοβε
In Greek for the date 2013 we say "δύο χιλιάδες δεκατρία" and not "είκοσι δεκατρία" The second version is completely wrong.
In the specific context that you gave you can use the verbs "έζησα" or "έμεινα" interchangeably. There is not an important difference in this context.
The questions "Πού ζεις;" and "Πού μένεις;", though, have a different meaning in Greek.
"Πού ζεις;" means "In which country do you live?" and "Πού μένεις;" means "What is your address?"
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Vasiliki Baskou, Instructor/Director, https://learn-greek-online.com.