Will 3" sanitary pipe be sufficient for the kohler k3427 toilet?

get a plumber in under warranty to fix

check for correct water level in the cistern
have a plumber clean out the lines as there may be a blockage in the pipe

sounds like something is missing. There are various models in the highline series, which one is it?

How to Fix Running Toilet

You cannot adjust the pressure on the toilet. But you can adjust the stop setting screw at the top of the float arm. If the water is coming in too fast you can adjust the valve where the toilet water line connects to the wall water supply. Closing the valve a little will slow down the flow of water and it will take a little longer to refill the toilet water tank.

Gerber avalance is a great toilet if you can find, is ada 18'' with seat

If I understand correctly, your water level inside the bowl is 3 or 4 inches from the top of toilet seat?
Sounds peculiar to have that water level since you would get splashing etc.
That is not sanitary, and would be a code violation.
Look at side profile of tank.
Look at porcelain behind bowl and you can see outline of "s trap."
This is the internal trap that each toilet has built in.
Purpose of trap is to a) set water level inside bowl and b) just like a sink trap, seal pipe from sewer air from entering home.
Photo shows trap on sample toilet, with line showing approximate level of water inside bowl.
Since photo is at an angle, the line appears to go downward instead of level. Again the line is approximation, and photo intended to show where you can look on your toilet.
Your tank should have similar s-trap feature. From the feature on your tank, you can see what level water is intended to be inside bowl.
Some more expensive tanks, outline of s-trap is not apparent.

If the water level is so high that you experience unsanitary conditions, this is a code violation, and toilet should be replaced.

Quick web search turned up Kohler contact page: http://www.us.kohler.com/general/contact.jsp
KOHLER Customer Care at
Phone: 1-800-4KOHLER (1-800-456-4537)
Hours: 8:00 AM - 5:00 PM (Central Time) Monday to Friday
You can refer Kohler to this link on Fixya so they can clearly understand issue.

replace the flapper

Check tank for fill line running from fill valve to overflow tube. It will be a 1/4 " line that allows the tank and bowl to fill. It should be connected from fill valve and connected at the top of overflow by a clip or hanger.

Check out the water level in tank to make sure it is filling to line on overflow or within 5/8" to top of overflow pipe.

You should use toilet seat paper covers. In addition to promoting sanitary conditions, the use of disposable toilet seat covers can also help your organization to save both time and money. When you consider the alternatives of toilet seats, it is easy to see how beneficial toilet seat covers can be. When visitors to your restrooms use the proper toilet seat covers, restrooms are more easily maintained.