"She has lived..." is correct. "This year" means from the beginning of the year, up to today's date, so the only answer is present perfect. Also, the next part of the sentence uses present simple. The timeframe stays consistent.

And just to add something to Peachey's answer: Remember that the present perfect always tells us something about the present time. In this case, you're giving an explanation about why she now knows a lot about different cultures. Her experience of having lived in these places has an effect on the present situation - hence the present perfect tense.