HELP ME if you were an illegal to EU

[onewhowishtostudyinspain]

Hello, I am new to this forums. Actually new to the "forum".
The reason why I intended to use forum is talk about my past problems with related sites which may be the help. It's a long story but I really need HELP.
Well here's my problem.
-I lived in Spain for over an year but as an illegal. I got two-years off from my university then flew to Spain. For my time being there, I studied Spanish and did some part-time jobs. In 2013, my university didn't give me another year off so i had no choice but come back. Then there's big problem arose. My cousin who is an american citizen wanted to visit before i went back to Mongolia. So we decided to go to France for a week without myself caught and she planned to go Italy alone and I had to come back Spain. But i did caught in border between Spain and France. So, French Government paid my plane tickets to go back Mongolia which was court decision.
It was exactly 3 years ago and I was 20 then. I graduated this June.
So now I wanted to go back to Spain to have my master desperately-
-Has anyone this problem?
-Will I ever could go back to Spain or any other EU countries?
-If I got accepted any Spanish university or Master preparation course, could I go back to Spain?
-I am sure that my history is visible to every embassy I would want visa to study Visa Required Countries, so what I can do?
-I really want to go Spain or any Latin american country to get my master because I really love spanish.
Please help me with my problem.
Thank you.