I limit this question to universities in Canada, UK, and the US.
I know that certain competitive universities required Ancient Greek and Latin for admissions, and also university study. For example, page 10 of 17 of this PDF states Oxford University's admissions requirement, of knowledge of Ancient Greek until 1920 and Latin until 1960. In general:
1. For admission, what rough percentage of universities required Ancient Greek and Latin?
2. Then what about after admission, during university?
For both questions 1 and 2, please roughly date your answers.
PS: This Quora answer moots this question for the US.
From the establishment of medieval universities up to the early to mid-20th century, 100% of universities required Latin. It's difficult to say when the requirement was dropped, because that depended on individual universities and regions.
Greek was not a requirement at most universities, but most students would have at least a smattering of it, and might study it at university.
Latin might or might not be studied at university. Students would come to university having studied Latin from an early age. They would already have a solid grounding in the language, Latin literature and classical history, but they might study them in more depth.
Often lectures in other subjects were in Latin, well into the 18th century, and books on other subjects might be written in Latin.