Can I request to see a reference about me?
As a general rule, institutions are very reluctant to give access to letters of reference to anyone and candidates in particular. That's because they know that if they regularly shared these letters with the people being written about, letter writers would stop giving honest assessments.
As a consequence, regardless of matters of law or regulation, you should expect that universities will not give you the letter. You may have a legal way to obtain such a letter, but you will likely have to sue the university to obtain it. Whether that's worth your time or money is a case you need to evaluate for yourself -- taking into account that knowing what is in the letter does not actually change anything. It's not like the university will offer you the position you were seeking just because you know what was in the letter.