In addition to Snopes’ excellent write-up, I think it’s important to note two more things.
First, the president of the United States cannot conduct impeachment proceedings; the House of Representatives impeaches the president, and the Senate determines whether they should be removed from office. This is also the constitutional procedure for other government officials. The Constitution gives the “sole power of impeachment” to the House of Representatives and the “sole power to try all impeachments,” and the Supreme Court has interpreted this to mean that the executive branch (of which the President is the head) is expressly precluded from impeachment proceedings.
Second, if Maxine Waters became president, then it means that Donald Trump is no longer the president, and therefore is no longer subject to the impeachment procedure. She wouldn’t be able to impeach Trump because he’d be just another private citizen. All former presidents, including Barack Obama, George W. Bush, Bill Clinton, George H. W. Bush and Jimmy Carter, cannot be impeached because they are no longer officers of the United States, just like how all other private citizens not working for the U.S. government cannot be impeached. (This does not mean former presidents cannot be prosecuted for crimes committed while they were in office, but that would not be impeachment proceedings.)