1) Build the tank with robust joints to begin with. You are basically building a cabinet. It's easier to look up examples of good cabinet joinery than trying to find how tos on plywood vivaria. I use pocket hole screw joints and glue. For aesthetics, keep the pocket holes on the interior of the tank and then fill them with dowels. Sand everything flush and fill any other small cracks or voids with a wood filler epoxy. Make sure the interior is clean and the surface is sanded/prepped to the standards that the epoxy brand you use calls for...
2) I use pond armor. There are other epoxy options but that's the only one that I've used successfully. I would absolutely go with an epoxy for this step. I have never used any fiberglass reinforcement for the joints. Fiberglass in the joints is done for fish tanks where the build will hold many hundreds or thousands of pounds of water, but I feel it's probably unnecessary for a vivarium that might have an inch or two of water in the bottom. But do what you think is best. Overbuilt is always better than underbuilt. 3/4" plywood is very strong and has very good dimensional stability for the tank sizes I have built. I haven't built any tanks larger than about 2.5 feet wide, 20 inches deep, 3 feet tall.
3) Silicone sticks to epoxy very well. Great stuff stick alright - probably about the same as to glass. When I'm going to use great stuff to cover the sides/background, I silicone a piece of egg crate to the epoxy first. This gives the great stuff far more surface area to cling to. I've never had any problems mounting heavy wood to the background using this method.
I'm not an expert by any means. I've built about 8 plywood tanks so far and change something every time based on what I learned from the previous build. Have fun with it. It can be a lot of work to do it right, but it will be something unique that you can be proud of. Here are a few my wife and I just finished up.
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