Very thoughtful and interesting piece on impeachment from the Cato institute. It explores what it means and how it has been used historically. Remember impeachment is meant to act as a fuse protecting the body politic. It's is inherently a political NOT criminal act. https://www.cato.org/blog/impeachment-impulsive-ignorant-incompetence
It's not inherently a criminal act but to get into enough hot water to be up for impeachment means you have committed acts that are statutorilly illegal.
Not necessarily. Read the article. Neither Andrew Johnson or the judges mentioned broke any statutes. It can be argued the Billy Clinton didn't either. Nixon certainly did. It can also be argued that Andrew Jackson not only broke the law but flouted the constitutional separation of powers yet he wasn't impeached. The common theme is that it's not whether laws are broken or not but whether a office holder has committed a politically unacceptable act/acts that convinces Congress of the need to act. As stated in the article the founding fathers left it vague enough to make it exceptionally hard to use but with enough elasticity to not rely on laws being broken to use.
That's very ambiguous. It just means if we can get enough support from people who don't like you we will impeach you. For whateve reason we can think of. What if a majority of senators had decided they didn't like Ronald Reagan chewing on jellybeans in the White House. Silly, yes but no more far fetched than a lot of things politicians do for real.