My new K-4632 AA toilet flushes fine and refills the bowl. The tank equipment works as it should. Problem is, the bowl completely empties in about 5 minutes and stays empty until the next flush. The water isn't leaking on or through the floor so it is clearly going down the drain. There must be a connection from the bowl trap directly to the drain. Older toilets didn't have that, but this one looks like a little passageway is cast into the toilet. I have another of these toilets and it works perfectly.

Water is not draining completely from the toilet line to the sewage tank. If there is a 'low/little slope' section anywhere in that drain line, solids WILL settle and collect there and cause water to back-up in the toilet drain line. Then the toilet will not flush completely or at all until the 'soft blockage' is cleared out and the drain line emptied. Al 'gravity drain' toilets require a free draining/empty drain line that allows flush water to drain unrestricted. A basement toilet has a pump that 'forces' flush water up and out with enough pressure to sometimes force out the 'soft clog.'

That's an interesting one! Does the flush valve close properly so the tank can refill? Does the float valve allow the tank to refill fully, to near the top of the overflow? That can be adjusted, if it doesn't.

Check fhe flush valve - you may have an obstruction under it. Also check the water port from the bowl side - feel up inside the port for obstructions or buildup of hard water deposits.

WASH YOUR HANDS THOROUGHLY afterwards.

replace the flushing controls or install a new cistern

The amount of water in any toilet bowl is determined by its construction and no tank adjustment will ever change that. American Standard has a history of having small water surface areas in their low or ultra low flush toilets. Take a large container of water and pour directly into the bowl. If the ending level remains the same, then that is the manufactured level for your toilet.

Not all tanks completely discharge all of the water when flushed. Measure 1.5 gallons of water into a container. Turn off your water supply to the toilet then flush normally. Replace the water in the tank with your premeasured amount and observe this new water level. You might be surprised to find it is at the same level it always is. Since water weighs more than 8 pounds per gallon, one concept used in todays toilets is to have more than 1.5 gallons of water in the tank and use the extra weight push the water past the flapper at a faster rate while designing the flapper to drop after only 1.5 gallons have passed through.

The flapper isn't staying open long enought, try holding down the handel for a few seconds each time u flush.

Sounds like your toilet is not vented properly. Possilbly something caught in the trap is causing it to syphon

Is it not refilling the tank or the bowl? I've got a toto also that is not fully refilling the bowl after each flush. No leaks or other problems. Tank refills fine. Seems that the flapper doesn't float long enough to allow a sufficient amount of water to drain into the bowl before closing. Any ideas?

Most likely, you do not have a good seal on the flapper valve at the bottom of the tank. To confirm, try this:
Turn off water and flush toilet. Then lift up the flapper valve and put a light coating of vaseline on the mating surface where it contacts the toilet tank when closed.
Turn water back on and see if it continues misbehaving. If that fixes it, it was a bad seal. Usually that is all it takes.

it sounds like it is not flushing completely at first and then releases and the suction is pulling water out of the bowl. Could be a venting issue or a clog issue that is hindering the proper flushing of the toilet.