[Silicone is not an option whatsoever. It is only effective with glass.
Weld-On #4 and #16 can be purchased from Regal Plastics or Allied Plastics. #4 will need the "needletip applicator bottle", and you'll need a glass turkey baster to get the stuff out of the can and into that tiny bottle. #16 needs a fine nozzle to control the flow, available at most hobby shops. If you don't use the nozzle, it will run out in a thick glob, and weaken your project. It should not be used like caulk, but rather as a fine bead in a seam for patching when #4 didn't work out.
Go to Reef Central's "DIY forum" and look for a thread by Zephrant called "Pins Method". That will teach you how to align and bond pieces together. Tape is unnecessary and impractical in my opinion.
You will glue all the walls and baffles together first and once cured, then you glue on the base. And after that is cured, then you glue on the top. Finally you route all the edges to make a clean looking sump and/or refugium.
It only takes a minute or two for a piece to stay in place, and I use Speed Squares as spare hands to hold pieces up vertically while the glue takes hold.
There is more infomation on my site about construction and routing on this page:
http://www.melevsreef.com/allmysumps.html]