After installing, the water level in the bowl filles to proper level then it drops down quickly. There aren't any leaks. I did not have this problem with the toilet that was their before. Any suggestions? I also replaced the wax ring twice.

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.'

check to see if waster continues to run into the bowl after the plunger has returned to stop water flowing. If it is a slow leak then replace the flush washer on the stopper plunger.

The bowl is cracked and is leaking down the drain. You will have to replace it. It may have cracked if the bowl hold-down bolts were overtightened, or the bowl was not able to sit flush (pardon the pun) on the floor. If the bowl rocks when it is first installed, instead of tightening the hold-down bolts, use a couple of tapered shims under the edge of it, then caulk to fill the gap and hide the shims.
Good luck.

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.

Check to be sure small tube is flowing inside the ovefow tube. This is the water that flushes the rim holes, and refills the bowl. If you don't have flow clean or replace the float valve.

Check the fill tube in your toilet one easy way to see if it's leaking is get food coloring and pour in your tank to color the water this makes it easier to see and squeeze the tube in the tank when it's full if you see the colored water running down the middle of it you have a winner! if not you can look around for it sometimes the plastic under the flapper gets cracked too

First off,If the air vent was clogged the toilet would back up and overflow and when it did flush, it would make a gurgling sound.
secondly the water level in the bowl is not important as long as it covers the opening,The water is only there to keep out sewer gases so they don't enter your home and the shape of the trap will always maintain the proper amount of water needed to prevent this.
The previous water level may have been due to a partial clog that has since been removed.

First, fyi, adjusting the knob? in the tank, or the fill level will not increase the amount of water in the bowl. The bowl fills to a certain point, and then as more water is added it starts to go over the built in trap, and down the drain. When you flush the toilet, all the water in the tank dumps into the bowl, and the existing water is pushed over the trap and down the drain. All of this being said it sounds like you may either have an internal crack, between the bowl and trap; you may have a crack that is draining under your toilet, (water spots?), or you have a more serious plumbing issue, improper venting, which is causing a vacuum, and pulling the water out. Hope this helps.

If very little water is used on initial flush, The bowl is functioning as a tank for second thorough flush. The high water level cannot stay high in the bowl while in motion or you would have a mess ion start and stops.

The tank holding the proper amount of water is a good sign. The inside of the stool is like the GOOSE NECK under you sink. It always holds water. This may sound like a bit of a hassle to do but if all 3 toilets are identical, here is what you can try if you are a bit handy. Go to the hardware store and purchase 4 toilet wax rings with a plastic flange and a few sets of toilet floor flange bolts(they are cheap and you can always return if not used, as It is better to have xtra parts on hand). Turn off the water supply to the "Mystery Toilet". Leave the tank and everything connected to the stool. Flush the toilet and remove all excess water from the tank and bowl. This can be done with a shop vac, sponge or towel. Disconnect the water supply to the tank. Remove the bolts holding the stool to the floor and carefully remove toilet. Scrap off all the old wax from the floor flange and bottom of stool. Now go and repeat this proceedure to one of the toilets that is working properly. In other words Switch the "Mystery Toilet" with a "Working Toilet" and see how they react. If the working toilet does it in the same bathroom and the "Mystery Toilet" does not do it in the other bathroom then you probably have a VENTING PROBLEM. If the "Mysery Toilet" Does it in the other bathroom then you most likely have a Defective Toilet. This Job is best done by 2 people, as it can sometimes be challenging to center the new wax ring on the toilet flange. Reconnect to the floor and reconnect water supply to the tanks. DO NOT OVERTIGHTEN BOLTS to the floor flange as you may crack the toilet. All drain lines must be vented properly for water to flow. If you are curious check out drain venting on the internet. Also, sometimes a vent can become obstructed with debris, ice, bird nest, etc.. I would 1st check the vent on the roof visually and then have someone flush and listen. If you believe the vent is clear....Then do the toilet switch and go from there.....Hope this helps and Happy Holidays....Joe