And that constitutes a much larger part of our lives than is traditionally acknowledged. Which is itself, also, a political matter, because designating a subset of actual politics as "officially politics", and then marginalizing that subset, is one way to slow down further political developments in that department.
No, its not.
"Everything must be directed by the coercive power of the state" is. The former does not imply the latter (the scope of the coercive power of the state is, itself, a political issue.)
Yes, actually it absolutely is. Putting everything up for grabs for state (or in modern day; the mob) control is literally totalitarianism. People who "don't understand" this are either abysmally stupid or are power mad imbeciles who are pretending not to understand for Machiavellian reasons.
If "everything is political" there is no room for private life, which is the only life that matters.