Edit Time_Forgot to Stop Timer

You can't do this with Garmin Connect. Some other non-Garmin programs may allow you to do this. You can also edit the tcx file, but to properly re-calculate the distance and times, you will have to run it through some another program. If you have a Mac, Ascent will allow you to do all this, but I don't know about Windows programs.

I forgot to stop the timer at the end of a race. Can I delete some of the laps/times once it is downloaded to connect?

Attach the tcx file to another post here and somebody will fix it for you. Tell us the time you want the track to stop.