No, Discord does not give others your location. Several users have complained that another user does know their location so it’s worth mentioning that while Discord doesn’t give your location, there are several ways to uncover it. It is also rumored that sending someone an image will send your location in Discord.
The easiest way to report someone on Discord is to simply tell a moderator of the server that the inappropriate behavior occurred in. If you want to report something to Discord’s own Trust & Safety team, you’ll need to turn on the app’s Developer Mode.