This is how I would revise it (US usage): Thank's for your encouraging email. As you predicted, they requested my resume when I registered with them. But their active recruiting period was over by that time, and so I'm not having high expectations of gaining an internship with ____ this summer.
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AnonymousI'm not having high expectationsI don't have high expectations
AnonymousIn a group you can discuss tricky questions withIn a group you can discuss tricky questions with others,theothers,
Anonymouseveryone contributing his wayeveryone contributing their
Raine HookeThis is an emailThis is an email to my ex-lecturer.writingto my ex-lecturer.
Raine HookeJust hope someone could give meI hope someone could give me hahelp by having a look on my grammar.