Here's some practical hints on application methodology.
Know your pH, first. If above 7.0, proceed with application. If not, rethink.
Alum comes in powder/granular form, or liquid. I like liquid. We apply with a pump, mixing alum 25-30 parts water per part alum. Spraying across the water, we observe several ways. First, we measure pH every 15-20 minutes, depending how fast we apply the material. Then, we watch the water. As inorganic matter (suspended solids/soils) begin to react, they flocculate, like dirty little magnets attracting to each other. Watch closely, you will see dirt begin to clot, then separate, then clot, then separate. As bigger "chunks" of solids form, you can see them grow larger. Stop applying, and watch. Check pH. As these small dirt clumps form, pH will show a temporary change.
Here's what you will see. pH the same, pH the same, same, same...then it begins to plummet, in areas where flocculation begins. Stop applying. Measure pH again. If it is lower than "normal", add hydrated lime cautiously, to bring pH back up. Did I say to monitor pH? Monitor pH.
Let the lake sit still, overnight. If still turbid, add a little more alum.
Using powdered alum? Mix it with water, then mix with lake water 25-30 to 1 and spray over the lake.
Don't have a pump? Get one. The mistakes you might make without it easily covers the cost.
Gypsum has similar effects as alum, but much slower, with considerably less risk.
Regarding ammonia, or ammonium, your water de-nitrifies it quickly, into nitrites and nitrates. However, alum can bind. My experience with alum tends to lean toward suspended soils mostly affected by the application. I haven't measured alum's affect on ammonia.
Alum works great, but risks are high. I would recommend using it, with proper caution. By the way, the stuff is caustic, be sure to clean equipment, boat motors, boat, etc., after use.


Teach a man to grow fish...
He can teach to catch fish...