Can you please correct my writing?

Dear Dr. X,

Thank you very much for your indications.

The word "indications" makes no sense. Do you mean guidance or advice? You quite logically began this line with an uncapitalised word because of the comma on the preceding line. I can't explain why but most people don't do that. This website has examples of English and Italian email formatting: http://www.oxforddictionaries.com/words/italian-sample-emails.

I would be grateful to you if can send me the filled form within April 7th because I have to consign it before my degree date (April 13th) and I need also sending institution tutor's signature.

I would be grateful if you would send me the completed form by 7 April because I must submit it before 13 April and I must include the section completed by you.

Have a nice Easter,

C.