Rarities/covers/b-sides?

there aren't too many to my knowledge.

There's a cover of Judas Priest's "Rapid Fire" recorded with Chris Kontos for a tribute album.

The Japaneese edition of "The Gathering" has a 12th song, which is "Hammer of the Gods"- an instrumental that had been intended as a regular song but wasn't finished.

The covers of Aerosmith's "Draw the line" and Scorpions' "Sails of Charon" appear on the "Signs of Chaos" best of album from 1997 (and also on the "Dog Faced Gods" single from 1994 if my memory serves me well).

Then there of course is the mighty "Reign of Terror" on the "Return to the Apocalyptic City" EP from 1993 (which also isn't a studio album).

The single from 1988, "Trial by Fire", contains different versions of "Reign of Terror", "Nobody's Fault" (the Aerosmith cover- the second version's on the "The New Order" album) and perhaps "Trial by Fire" (I'm not entirely certain whether all three of these songs are in different versions or not- the title track probably isn't)

The single for "Electric Crown" contains 2 versions of the song, but the second one might just be simply a shortened version (maybe the videoclip one)- just like the version of "Return to Serenity" from the aforementioned "Return to the Apocalyptic City" EP is just a shortened album version

"Live at the Fillmore" has 3 ballads (Return to Serenity, The Legacy and Trail of Tears) in acoustic versions. You probably know these, but it's still definitely worth listing.

I also recall a Kerrang's split with Acid Reign from 1989 or 1990 which contained "Greenhouse Effect", but I'm not sure if it was a demo/alternative version or just a live track.

And that would be pretty much it when it comes to rarities released by the guys under the Testament banner. No B-sides, no demos/garage/instrumental/extended versions were ever released...unfortunately.
 
I'm pretty sure I heard a "Seek and Destroy" Testament version somewhere,sometime...

it´s also not TESTAMENT it´s only Chuck Billy, it's on a METALLICA tribute record with various musicans (Chuck Billy, Billy Milano, Eric A.K, Robert Truijo, Dave Lombardo, Lemmy Kilmister... )

Chuck Billy sang also on a Maiden tribute record the song FEAR OF THE DARK
 
on the video "Seen Between The Lines"which has since been released on dvd..Eric sings and plays a cover version of the Exodus song "And Then There Were None" Backstage before a show..very cool version too... check it out...