The verb which comes after the auxiliary verb - "did", always will be the base form (that called "infinitive" form, meaning without any inflection to the past tense). Therefore: I did not go to university yesterday.
Fatima is not at home at the moment, She . . . . . . . . work.
The preposition 'at' can be used in multiple contexts, such as telling time or location (e.g., telling someone to meet 'at midnight' or 'at the coffee shop'). However, 'at' can also be used to introduce prepositional phrases that identify the object of a sentence.
Example: He was looking at all the different options.
Have been and has been are verb constructions that are used in the present perfect tense and the present perfect progressive tense. We would use have been when the sentence subject is I, you, we, or the third person plural.