The correct answer to this open question is the following.
It seems that your question is a little confusing. It seems that you superimposed the terms and there are many questions in one.
However, trying to help you, we can share the following.
The system of checks and balances allows the president to veto legislation passed in Congress. The check that the executive branch has on the judicial branch is the power to nominate a justice to the Supreme Court.
In the United States political system, Congress or the legislative branch as part of the blueprint for checks and balances has the power to impeach and remove public officials, including the President.
The checks and balances system was designed by the framers of the Constitution so none of the branches could have more power than the other two.