Sorry to hear about your log-in problems. Is there a way to retrieve your password and/or user name? That's really odd that it won't mask the password.
Whenever I download music into Zune, it shows up in my Groove library as well and is playable there. Groove builds its library from watched folders, including Zune's. If it's not set that way, it can be. For awhile Groove wasn't keeping up with my Zune downloads, having stopped halfway through the Zune library and not building any further. Now it seems to be keeping up, at least with the newest downloads. Unfortunately the reverse is not true -- you cannot play (or sync to Zune players) DRM files downloaded in Groove using the Zune software. They are incompatible in that direction.