That is odd the bottom had two pieces, though I've heard of it before. If you are willing to spend the money I would replace it with one solid piece. Was there any water in the tank while it was outside? Water freezing in the tank would put stress on the seams, pushing them apart. Also large swings in temp could stress the silicone. It really isn't hard to damage silicone to the point it gives out. Also on the foam, is the tank rimmed or rimless? Rimless the foam was a good idea, if it has a rim around it foam does you more harm than good. If the stand has a wobble you need to shim it under the stand, dont use foam to level it out as that is how you twist your tank causing more stress on the silicone.
After you take the tank apart all of the glass must be cleaned very well, acetone works very well for this. You must use more than just a razor blade and water as that will not be clean enough for the silicone. The glass should be squeaky clean. Honestly getting it clean will be the biggest part of this project. A tank this size is going to take you hours of work if you do it properly.
If you wanted to get new side pieces you certainly could. Once the glass is cleaned up it will be no different than glass you buy at a shop.
As far as assembly goes, the process is tough and must be done very, very quickly. ALL of the silicone must be done at once, you cannot inject silicone after some has cured, that is terrible advice. Once silicone has skinned over, which takes between three and five minutes, it will not stick to itself. You need one continuous bead of silicone for every seam, all connecting in the corners. There can be no gaps or you will have leaks or a blow out. A tank this size I wouldn't bother with spacers, the glass just isn't big enough to worry about squeezing all the silicone out, especially at 1/2".
You are going to want at least one other person helping, maybe two. Depending on if you build the sides on the bottom or around, you will want to do the silicone around the bottom, add the front or back piece, silicone the two sides where it meets, add the side pieces, then silicone the last side and put it into place. At this point you need to clamp the glass, do not use tape to hold the tank together, it will not be stable enough. If the silicone slides at all once it has skinned over you must start over as it will not cure properly. Then you silicone the inner corners. This must still be done in the three to five mins so it cures with the rest. Run a bead up each corner then using a wet finger form it into shape.
It is a boat load of work for such a short time, on a tank this size you have your work cut out for you. Be sure to use a good silicone. No matter what anyone tells you GE I or II is not good silicone, that stuff is garbage for building a tank. I would recommend Momentive RTV 103 or 108 depending on if you want black or clear. You can get either through the Grainger website.
As a side note, 1/2" is a bit thin for a tank that tall in my opinion, so place make sure the top is braced properly. Hopefully this helps a bit. You have a big project on your hands.