As for your Social Security tax withheld, you need to go back to the university and ask why these taxes were withheld. Note that this exception does not apply to all students of the university; some people that you might consider to be students don't actually qualify.
Please see "Student Exception to FICA Tax" at the IRS website, and especially read Notice 2005-11.
Note that "FICA" refers to both Social Security and Medicare taxes together.
The university may point out why it believes that they were required to withhold FICA on your pay. Note that since the university as employer is also paying an equal amount of FICA taxes on your behalf, they are actually motivated to agree with you and not do the withholding. The fact that they did the withholding makes me think that you don't meet the exception that allows you to opt of of the FICA withholding.
So, ask for the reason in writing from the university on why they did the withholding. On form 843, you will have to explain why you think that the university was not justified in doing the withholding, so in all fairness, you need to ask them.
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