What is the problem when water is running on a dual flush toilet

Raise the level of the water. The dual flush water levels are minimal by design, but need the full flush volume of water. There should be a level line inside the tank, go about a 1/2" above.

A dual flush toilet is a fantastic option to save water and make your home more environmentally friendly. Giving you the option for a half flush or full flush at your discretion, you can lower your water consumption while still getting the job done. However, like all toilets, they can present problems that mean the toilet doesn't function as it should. One common problem in dual flush toilets is constantly running. You hear the tank constantly being filled, even when it should be finished and completely full. If your dual flush toilet is constantly running, first check for the top three problems that cause this trouble:
Flapper or Seal Trouble
The flapper or seal is often the culprit in constant running water in both normal and dual flush toilets. Over time, this rubber piece may become brittle or simply misaligned. To check it, turn off the water supply and flush the toilet to completely empty it of water. Remove any remaining water with a sponge or towel. Then, you'll need to remove the flush valve canister in order to access the seal. Once you've found the seal, check to see if there are any cracks in the seal. If there are, you'll need to replace it. Otherwise, check to see if it can be re-aligned to sit nicely in its place. Some homeowners find that applying a bit of Vaseline to the seal can renew it, making it supple and functional again for a while at least.
Debris
Sometimes the water supply isn't as clean as we think. Or, dust and dirt may be able to enter the toilet, causing the fill valve to malfunction. To check it, turn off the water supply and remove the lid from the fill valve. Then, look for any debris and remove it. You may also consider brushing out the valve with a small brush. Once you're certain it is clean, recap the valve and check if the problem has been solved.
Broken Zip Tie
The fill valve in most dual flush toilets has a zip tie to keep the base of the fill valve in place. If the fill valve isn't strongly secured, it can cause the toilet to run. Sometimes these ties wear out or break before the rest of the device does. You'll need to replace a broken zip tie with a new one if you find that it's broken. If possible, you can place two zip ties on the fill valve in order to assure that the base doesn't wobble, causing the leak. Many times these problems are easy for the average homeowner to check for and repair. In the case that you are not able to find a solution to your dual flush toilet's constant running, then you'll need to call in the help of a professional plumber. A high quality plumbing company will be able to help you troubleshoot your dual flush toilet troubles and make sure it's functioning properly again.

Check flapper valve in tank

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The flapper at the bottom of the tank is leaking and needs replacement.

Make sure the small toilet fill tube in the tank is still running into the tank overflow tube.

Why do you want to change it out just because it doesn't take paper out ? The problem is in your trap. Don't change it unless you just want to. I don't think you can change it over anyway due to design differences.

Adjust the float on the Fluid-master a little higher if possible. This should allow more water to enter the bowl after the flush.

your float is stuck

If this is one of those models that most people have, the valve that shuts the incoming water off when the tank is filled is probably bad. It only costs about 8-10 dollars to replace. This valve is actually a stem or tree shaped device.