ludiNano,
here is my $0.02 for what it is worth,
This system is capable of running anywhere from a trickle to over 2000 gph as the OP configured it. So 800 gph would be very doable through 1" plumbing. The concern (depending on many factors) would be possible noise, though I think it is unlikely that you would have a noise issue at 800gph with 1" plumbing, I think you just have to watch out for your adjustment on the non-syphon line so that it didn't get too much water under normal operation and thus create noise.
I am no glass expert...but, I made my 5"x10"x24" external box out of 1/4" glass and it feels plenty robust. So I think that your dimensions of 5x5x28 would also be suitable for 1/4" glass.
I used RTV 103/108, which is a reef safe adhesive, not just a sealant/caulk, it's better suited for constructing aquariums and in this case external overflows. (you can search this site for silicone and find it mentioned many times.)