This is a long one.... First off you do NOT need to be a resident to own PGYan real estate. any person or entity can own real estate. They will need to be present personally to sign paperwork with the attorney to start and then end the transaction.
No real estate agent is needed, in Paraguay the buyer and seller can sit down and negotiate their own deal out ...
No, you cannot travel outside the Schengen area without a valid passport. Likewise you cannot enter the Schengen area without a valid visa, unless your passport allows you visa-free entry into the Schengen area.
You can take classes at La Universidad Autonoma de Asuncion
I also found these two classified adds:
I had better luck searching in Spanish instead of English. Try searching for
aprender español en paraguay
español para extranjeros en paraguay
escuela de idiomas en paraguay
if you have chrome, the browser will ask you if you want to auto-translate ...