I would like to know how many times a user control is being used in a sitecore site. If possible, I would like to get the list of pages that use a specific user control. Googling doesn't seem to help.
You can look up the referrers of the specific user control since it's an item in Sitecore (rendering/sublayout) using the Link database.
For a quick check, you can take a look at the Navigate ribbon > Links
If you want a report-like list, it might be easiest to use Sitecore Powershell Extensions to get a list of all referrers in an exportable format - https://doc.sitecorepowershell.com/appendix/common/get-itemreferrer