Keep in mind that your filter has to go into place all at once with many different walls and silicone mating on different panels simultaneously. I count 5 seams on the back wall, one seam on each side wall, and 3 seams on the bottom. With silicone, if you are not able to run the seams, they all have to touch simultaneously and not move after placement until they cure. If you touch one side and then slide it, you will lose the seal unless you are able to run the seam with your finger or a tool and push the silicone back into place creating a cone over the corner. It's practically impossible to insert your setup as shown and maintain the necessary seals. (not to mention running a line of silicone down a 3/16" wide acrylic edge). I would suggest fabricating everything as a box ahead of time using a piece of acrylic as side and rear walls. That will be a lot easier to assemble. Then insert the entire box into the aquarium and silicone the box in place. Don't use the side walls or rear wall of the aquarium for any type of seal.
Also note that your tank has a top frame with an inner lip making your opening to insert the filter smaller than the inside dimensions of the aquarium. You will likely need to either remove the top frame first in order to install the filter and then reassemble it or make the entire filter box smaller by enough space to fit inside the inner frame lip.
As far as biological capacity, I have kept 10 and 20 gallon aquariums with literally dozens if not hundreds of fry and juvenile fish in them with just a simple sponge or mattenfilter. Having more than necessary biological filtration does not make the system any better. But surface skimming is something that you can really only get from a sump system. Whether it be internal or external. You need that weir for the water to drop over.
Also note that your tank has a top frame with an inner lip making your opening to insert the filter smaller than the inside dimensions of the aquarium. You will likely need to either remove the top frame first in order to install the filter and then reassemble it or make the entire filter box smaller by enough space to fit inside the inner frame lip.
As far as biological capacity, I have kept 10 and 20 gallon aquariums with literally dozens if not hundreds of fry and juvenile fish in them with just a simple sponge or mattenfilter. Having more than necessary biological filtration does not make the system any better. But surface skimming is something that you can really only get from a sump system. Whether it be internal or external. You need that weir for the water to drop over.