Keep the old one.
The red thing is to release the spring when installed. Or is it a distance piece? Anyways, no need. Not necessary at least on the original which is always superior unless very worn and yours isn’t.
The shoe screws in with a small inbus (hex) in the part that has the adjustment spiral. It may have a detent in the spiral, you‘ll figure it out.
That’s good but I‘d rather have that as a spare unless something is wrong with the original. But that’s just me - I hate new parts!
Transfer the dowel to the new tensioner. And take a good look at the supply hole size in both the dowel and the tensioner body.