Part #15 and 16... is that needed or do I just need the barrel nut?

Barrel extensions are usually already installed on barrels except If it's a custom barrel and they'll let you know that It doesn't have a barrel extension.

You just need the barrel nut if your barrel does not have it included, when bought as a barrel assembly they usually include the barrel nut and delta ring assembly.


ETA:

Here's a photo of my barrel's M4 feedramps type extension on my Denny's Guns/ GTS Operator mid-length mid-weight barrel.





Ref: The OPERATOR Barrels thread link

Thanks..got it.