Is there a significant difference between "på/vid universitetet"?
"Vid" means "close to". I would say "på" means it's physically on top of the university.
Why is "by the university" not an accepted answer?
It is now.
How do I get the difference between "shall" (wishing/thinking about) and "will" (real planning) in this case? Or how can I make a difference regarding this in Swedish?
If you want to say "next to the university" do you use bredvid ?
Yes, bredvid means ’beside, next to’.
Is laboratorium an irregular noun? Sounds strange that the definite form is laboratoriet (not laboratoriumet)