Is earth part of milky way?

We live in one of the arms of a large spiral galaxy called the Milky Way. The Sun and its planets (including Earth) lie in this quiet part of the galaxy, about half way out from the centre. 100 000 years to cross from one side to the other

100,000 years to cross from one sideā€¦ What about the time where astronauts travel to each planet?

It depends on where the planet is.
Voyager 2 took about twelve years to reach Neptune. As of the time of updating this article in January 2022, Voyager 2 is the only spacecraft to have visited Neptune.
between 150-300 days
The total journey time from Earth to Mars takes between 150-300 days depending on the speed of the launch, the alignment of Earth and Mars, and the length of the journey the spacecraft takes to reach its target