Inquiries about my non EU spouse accompanying me as a mobility student

Dear Expats,

I hope you can help me with my following inquiries. I will give you the context of my situation.

I am an EU citizen (Italian) actually residing in Argentina. I will be doing an Erasmus Mundus Joint International Master, which takes place in three different countries (one semester each), Belgium (Ghent University), Poland, and France. My spouse (non EU citizen, Argentinian) will accompany me during my studies (I understand her movement is covered under Directive 2004/38/EC and that she can legally stay with me, correct me if this is wrong or confirm me this is right). If I am not mistaken, I should apply for an annex 33 residence document (mobility student) once I arrive in Ghent and acquire housing, and so does my spouse.

1) Does this residence document I acquire as an EU citizen in Belgium allows me to also stay in Poland and France for six months in each? Or when I arrive in Poland and France I need to do the same procedure? Does this also apply to my spouse?

2) Does she need to apply also for annex 33 in Ghent or what type of card is issued for a non-EU spouse of an EU mobility student?

3) Does my wife's residence document allows her to work in all of these countries during the duration of the programme?

4) It is possible that my wife will need to return to Argentina for six months without me. Is she allowed to do that and then return to the EU, supposing she already has the Belgium residence document?

Thank you for your time, consideration and all the help you provide. I hope you all have a nice day.

Kind regards,

Maximiliano