20 Most Recent American Standard 735083-400.178 Tank Cover F/4112, Black - Page 8 Questions & Answers

This sounds like the air switch in the motor is not working properly. You will need to remove the pump from under the tub to access the air switch located in a housing on the motor.

Replacement Air Switch will cost you about $20US Parts Center

Two things come to mind, The sinks were installed out of balance and way over tightened causing a constant stress on a warped surface, or a foreign object was left under lips of sinks. If they were purchased and installed at the same time you could have received damaged merchandise.

probably hair stuck in the drain. did you remove the stopper "pop up" if no hair or blockage there or in the trap, then its further down, you will need a small snake. 1/4 inch cable works well in bath and kitchen drains.
you can purchase one at home depot.

You may have to use a really neat tool and that is aunt splitter. You can get it at O Reilly's auto store or any of those stores. That should remove it.

There is a clog in the line. A plunger usually solves this problem, but you have to use a toilet plunger. Your local hardware store will give you the right tool ($13). If the plunger doesn't work, you need a toilet auger (also called a closet auger), which you can buy for less than $20.