Hello, my name is ***** ***** I will be the immigration attorney helping you today.
I am so sorry about your father. My deepest condolences to you and your family.
Under your circumstances it is possible to file for employment authorizations while on F1 visa. It is also possible to ask for a fee waiver. There is no guarantee that either one will be approved, but you can make a case for it. Sending it in with a fee waiver sometimes does delay the processing of the I-765, just so you are aware.
To apply you will send form I-765. To apply for a fee waiver, a long with your I-765 application and supporting documents, you will have to send the form https://www.uscis.gov/i-912 For all the supporting documents that you will need, you will have to contact your designated school official who can guide you on exactly what you need. This page from another school sets it out pretty well http://internationalcenter.umich.edu/immig/fvisa/f_emplsevere.html
Good luck to you during this process and I hope this answer has helped you!
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