TPU is a flexible filament that you can print with. It's better to print flexibles with a direct drive extruder, the shorter the path the extruder has to push the filament, the less likely it is to bind up.
You can print flexibles with a bowden extruder setup, but mostly just the 95a shore hardness stuff, because the softer stuff will just jam up. Shore hardness is how soft/hard the filament is, 95a is about like the sole of a shoe, and the most common rating for most TPU filaments.
Watch some videos before you start getting into TPU, it's alot different than PLA and ABS. For instance, it's recommended to turn retraction completely off, so there's less chance of the filament jamming inside the extruder. That leads to major stringing that you'll need to deal with at the end of the print. Also, a flexible build plate isn't going to help at all, because the print will flex with the build plate lol. That was a fun one to learn my first print.
Awesome material to print with though, you won't regret learning it
Acetone welding small stuff together is usually ok. My helmet is ABS and was printed in multiple pieces, I acetone welded the pieces together to hold them in place, then did a rough wet layup of fiberglass on the inside. I'd recommend you do something similar with your chest piece, just so you don't have to worry about a badly welded seam or anything. I took some pictures of the process and put them in my build thread here: MBDs Preator Suit