A moving car has a core that is active, i.e., the engine. Is a car alive?You must be registered for see images
The magnetic field is a simply way of me showing that the planet is not dead. The core is active thus activating a magnetic field shielding it from solar wind and other dangerous particles coming from supernovas, quasars and such threats.
Why in the world do you start comparing it with the rest of this solar system? Planets after mars are all gigants with some special properties, but the main source of life is light. They are simply to many Astronomic units far away.
Mars core is not as active as before since all vulcanic activity has stopped, thus making it clear that without a magnetic field the solar wind destroys the oppurtunity for proper life to exist.
Jupiter on the other hand has ultra extreme weather and the largest magnetic field, streching almost to saturn. Its protection is very dense but since its orbital rotation is 13.3 km/s the days are short, and its a 9 hour day my friend. Saturn is similar in weather and almost in size. But remember that jupiter quite big on the centre for the sole purpose of balancing the orbits and to swallow threats like comets .
OF COURSE earth is alive, what do you really think life is about?. It is everything, connections. The earth is just another exoplanet placed on the perfect place. Moving through the void of space with its momentum, perfect speed and Gravitational force.
Life cannot be given or "donated" if the donator himself is not alive.
Also, none of that shit about Jupiter and Saturn answer if they're alive or not. You know why? Because none of that shit is the qualification for life. Life has 7 qualifications, none of which you have mentioned.