Ted,
I am going to go back down one level from Snipe's excellent advice.
As regards your first question about alum being dissolved or staying suspended:
Imagine putting normal table salt in a glass of water. At first you will see the salt grains settle on the bottom. If you stir it vigorously, the salt will swirl up into the water, and after you quit stirring, a little bit less will be showing on the bottom. Eventually, if you stir it up enough, ALL of the salt will be dissolved and "suspended" throughout the entirety of the water volume in the glass. (We don't actually use the term "suspended" for dissolved materials, that term only applies to discrete particles that remain in a liquid. Also, it is possible to add more salt than your volume of water is capable of dissolving.)
Since you don't want your alum "settling at the bottom of the glass", that is the reason you use a slurry of alum and dump it in the pond slowly and try to spread it rapidly with your propeller wash, etc. If you just dumped in a 100# of alum as golf-ball size chunks, it would sink to the bottom and only very slowly dissolve into your pond water. (And the chunks that sank into the bottom sediment might never dissolve.)
Your next question about things sinking right away refers to the tiny clay particles when they flocculate. (That is just a $2 word that means clump together.)
Have you ever pushed two bar magnets together trying to touch the + end of one to the + end of the other? You can actually feel the magnets repel each other. That is exactly what is happening to the tiny clay particles suspended in your pond water. They have a tiny charge and are repelling each of the other particles.
Once you get the alum dissolved in the pond, a positively charge Aluminum ion will bind to a negatively charged clay particle. It then becomes a neutral particle. These particles are now a little bit sticky. As they swirl around in the water, these particles bump into similar particles and stick together (flocculate). As the clumps grow larger, they sink to the bottom of your pond much more easily.
As for your final question about a half treatment being able to clear half of the suspended clay. Experience shows us that it just doesn't work that way.
Imagine the mice chewed 12" of insulation off of a wire in your truck. It is now touching the frame and causing a dead short. If you wrap tape on 6" of wire, it does not solve the problem, your wire is still going to short.
Even if you knock the negative charge off of half of the clay particles in your pond, they will still stay suspended. They need to clump together with the other particles to drop out of the water column.
I hope that helps understand the "reasons" a little bit more. If not, then Snipe is an actual pond expert. If you just follow his advice, that is usually the best way to get your problem solved!
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