Well, it is impossible against 3c5, and probably not good against 3 cxd5 or 3 e4
Tarrasch defense against any third move from white?

Tarrasch defence is indeed playable against any "normal" moves by white.
U can even play Tarrasch set up against any white system, like english, 1.Nf3, 1.f4, etc...
If you mean 1. d4 d5 2. c4 e6 3. white moves c5, then you can play it for everything except obvious stupidities like 3. b4 so it is good to go against Nc3, Nf3, g3, a3, f3, b3.

As long as you're okay with the possibility of being saddled with an IQP, in some lines.
I tend to prefer the QGD Orthodox and/or Semi-Slav Meran (developing more minor pieces before the ...c5 push, so that any central pawn trades can be recaptured with a minor piece), just to avoid having to defend an IQP.
But some players don't mind IQP positions. So it's a matter of taste.
The Tarrasch Defense happens when 3. Nc3 c5 is played in the Queen's Gambit Declined. Is the Tarrasch setup (3... c5 in the Queen's Gambit Declined) good against most of white's third moves, or are there third moves from white where I shouldn't play 3... c5?
Following on that, are games in the Tarrasch Defense different from those in the Pseudo-Tarrasch Defense?