Your description is not accurate enough.

-No idea what happened to the 3spd. (That means a hub gear, right? Don't know about those.)

-The fixed hub most likely is a "suicide hub", ie a threaded freewheel hub with a track cog spun on. The cog prolly just unthreaded from it. No damage done if you're lucky, you just have to tighten it down super hard. Do inspect the threads and see if they're damaged. You can run a suicide, but a track hub is preferable, of course.