Hooker Comp Headers

Does the centerlink actually pass through the large gap in the drivers side header?
Yes
How do I remove that centerlink?
You need to take out the cotter pins and remove the castle nuts. (OK, duh) Then a pickle fork as there commonly called here is placed at the parts meeting point and struck with a BFH, a baby sledge should do the job.
Place the car up as high as you can get it so striking the fork with the hammer is easier to do.

The fork is not what I would call a special tool, but one everone should have to service front end parts or in your case, for headers.

Instalation is just put parts together and tighten down the castle nuts and cotter pins slide in and splayed.