Does anyone know any forum, FB group or other platform where students from different univerisites would exchange academic literature available in their libraries?
On Twitter, there's the #ICanHazPDF hashtag. Wikipedia explains:
Users request articles by tweeting an article's title, DOI or other linked information like a publisher's link, their email address, and the hashtag "#ICanHazPDF". Someone who has access to the article will then email it to them. The user then deletes the original tweet. Alternately, users who do not wish to post their email address in the clear can use direct messaging to exchange contact information with a volunteer who has offered to share the article of interest.
This 2013 article has some more information about the practice, including estimated usage figures and demographics. According to the data presented there, 24% of #ICanHazPDF users are students.
On Facebook, I don't know of any groups devoted to sharing literature, but I've certainly seen a lot of (successful) requests on my Facebook feed along the lines of "Can anyone get me a copy of this paywalled article?".
It's also worth noting that, if you are already a student with access to a university library, the library itself can provide you with interloans or copies of material from other libraries worldwide. As a university student, you have access to people who are literally paid to help you find the literature you need. Don't ignore that resource!