może lepiej:
I'm a student of ... at the Jagiellonian University in Cracow
...of DOING the internship ...
>I am looking forward to have a reply from you< nie brzmi dobrze (pomijajac koncowke -ing)
lepiej - 'I'm looking forward to your reply' (~to hearing from you - tez bylo dobrze) albo takie bardzo eleganckie "I would appreciate a reply at your earliest convenience"
>As an annex I attach my curriculum vitae.<
a nie lepiej 'I enclose a detailed curriculum vitae' ???
MADAM (nie madame)