Once again, many thanks for your help poconojoe and everyone else who has been so helpful to me. Brian M.You got the basics.
No filter after the bog. As mentioned, if you did add a filter and it clogged, your water would be backing up and overflowing out of the bog.
If you decide to drill any holes in the "tub", I would advise the use of a bulkhead fitting for a perfect seal. I think I mentioned that before.
There are a couple ways you can build your under gravel manifold pipe. You can drill holes or cut slits in your manifold pipe. If you cut slits, cut them 1/3 through the PVC pipe. I spaced mine 1-1/2 inches apart. I have two manifold pipes each is around 10 feet long. Since your setup is much smaller, you might want them spaced closer.
You can face the holes (or slits) up or down. It seems to be a matter of opinion on that choice. I faced mine up, figuring they might get blocked if any sediment collected on the bottom.
I have a clean-out stack at the end of each manifold pipe. (I have two manifold pipes). The end of the pipes have a 90 degree fitting facing up. The pipes end just above the surface of the gravel. I have a screw cap on each one.
If the water returning to the pond slows down, I'll turn off the pump, unscrew the cap, turn the pump back on and watch black water shoot out for a few seconds. (I shoot it into a nearby flower bed). This forces out anything that may have collected inside the manifold pipe. After that, the water runs full force.
I keep a rope tied to my pump for easy removal and to keep it off the bottom. This prevents the pump from picking up heavy debris that has settled on the bottom. I use a net to scoop that stuff out.
Oh, the water traveling through your bog should be relatively slow for best filtration.