I own a fiesta ST 08 plate and I am wondering what is that can looking part that the original air intake is spliting to before going to the air filter. It looks like the AC drier (not saying that it is the AC drier just it reminds me of it when looking at it). I have no idea what it does and do I need it? It is placed underneath the original air intake pipe and the splited hose goes straight in it underneath

That sounds like the "resonator" for the intake, basically like a muffler to reduce noise.