What is the term of office for a president?
Four years. A president can be re-elected once for another four years.
Who by law determine the removal of either the president of vice president during their term in office?
You are probably asking about "two terms in office." In America, a president is only allowed to be elected twice. Each presidential term is 4 years. So, a president, if he is elected two times, is said to be a two-term president, or it is said he served "two terms in office." (The word "office" refers to the Office of the Presidency.)
Section 1. No person shall be elected to the office of the President more than twice, and no person who has held the office of President, or acted as President, for more than two years of a term to which some other person was elected President shall be elected to the office of President more than once.