That is my old Y-pipe. It is a shoshop/BAT. I bought it from BAT who at the time had them made by shoshop. The reason I got it from BAT is because they actually had them in stock and were much more reliable.
Now...it is in fact welded together. The clamps that come with it do a horrible job of keeping exhaust gases in..they always leak. I can tell you for a fact that the flexpipe leaked when I sold it to the last buyer. I actually installed it on his car for him. You might want to put a new flexpipe on there. They're cheap from any autoparts store.
I think you need to keep on learning more about cars because if you crawled under and looked...it would be VERY, VERY obvious how this thing hooked up.
Also, do a little research. Go to this link and look at page 33.
http://64.202.180.37/files/contour.PDF It looks identical doesn't it?
Good luck.