They both are technically "correct"(because in order to be correct they need a noun after them), but it would be better if you said "at a university" or "in a university".
The correct preposition is...In the HQFor example : meetyou in the HQ
The preposition "to" typically goes with "according". For example, "According to the latest research, exercise has many health benefits."
Past preposition.
"On the internet" is correct.
The correct sentence with the correct preposition should read: "We climbed the hill slowly."
On
No, not every preposition requires an object. Some prepositions can function alone without requiring an object to complete their meaning. For example, in the sentence "He walked up the stairs," the preposition "up" has an object ("the stairs"), but in the sentence "They waited for hours," the preposition "for" does not have an object.
i am at the bank
on
after a preposition
It is correct to say a university.
To