I looked at the Research Assistant badge bit but couldn't understand how that works. It says 50 tag wikis but doesn't explain what it means. Does it mean editing tags on one site, say unix and linux stackexchange or 50 tag edits from different sites/corner under stackexchange banner ?
If you click on a tag, each one has a short description and a long description (for many, of course, it's currently blank). That's the tag wiki.
I'm pretty sure all badges are per-site. So you need to do 50 on any site you'd like the badge (and you can earn the badge on multiple sites).