Says it stands alone but it looks like I would need the whole EDD program running all the time burning bandwidth with sync checks every 15 minutes.
If you want to use EDD voice control then you need to be running EDD, yes. If you already have VA then you don't need it unless you're looking to replace that. Settings panel allows you to turn the EDSM/EDDB data pulls off or limit them to areas of the galaxy you are interested in to reduce bandwidth.
Do I have to update EDSM to get credit for any first finds I might make?
If you want to be the first to submit to EDSM then, obviously, you have to submit to EDSM. This has no impact on in-game tags.
How do I stop it from scanning my screenshots every 15 minutes?
Settings tab again, uncheck the 'Enable Screenshot Conversion' box and EDD won't do anything with your screenshots.