Hello, please see the below answers:
1st - Since my visa is going to expire in August, could the immigration give me an extension of my visa until October?
You need to provide a valid reason to the Immigration officer to extend your visa further... Could you not enroll in a new course OR in an existing one to extend your visa for another year as a student ?
2nd - If yes, I am traveling to Paris with him in September, would I have any problem coming back? By that I mean entering the State?
If your visa is due to expire in August and you go out of the state in Sept, you will NOT be able to return to Ireland, even though you wouldn't be able to board from the French airport...So be careful.
3rd (and last, I promise) - In November, we are going to Brazil for a couple of weeks, and we are planning to apply for the Stamp4 EUFAM in October yet. Would the immigration give me a temporary visa in the meantime? And how long does it take until they give me that? (Remembering that I will be a visa required at that time)
If you apply for the residence card in October, i think u would be on risk to go to Brazil in November as the EU Treaty rights section can take 6 to 8 weeks to return your passport and a temporary 6 months stamp (IF ALL THE DOCUMENTS ARE IN PLACE). The EU 1 application will take 6 months for the final decision.
MAKE SURE YOU PROVIDE ALL THE DOCUMENTS TO IMMIGRATION ON TH E FIRST PLACE WITH THE EU1 APPLICATION, THIS WILL SAVE YOU ALOT OF TIME.
Please find the EU1 application form on this link :
http://inis.gov.ie/en/INIS/Form%20EU1.p ... %20EU1.pdf
And make sure you have all the supporting documents mention in "Section 4". It wouldn't hurt if you go through the whole application form once to make sure you full fill all the requirements.
Good Luck