Surfing Waves

Hood swiggler, since your fin is swiggling too much, you are definitely doing something wrong.
The usual way of putting these fins in is to put the back part with the metal tabs in first. There is usually a gap in the plastic sides of the finbox into which you can slide the tabs. the plate for the locking bolt at the front of the fin also slides into the horizontal grooves. That gap must be there as you got the plate in.
Sometimes in manufacture the box or the fin are not quite standard in dimension and a little sanding ( best on the fin ) is required.

No worries, FIXED,

Have a look at the actual fin box the BIC bagging in the manufacture may have caused the walls of the box to be out of parallel.

Maybe even try another fin first before you do anything.
The hump specifically under the back of the fin may be too deep.
If the thickness of the side is too great try to ensure that you take off the excess equally so your fin will sit straight!

STOP! Take it to a surf shop. The have quick fixes for everything. It might be a small dent in the fin box, or something else. Shops love to help

Lol the answer to everything..."elbow grease"