If I leave my iPhone at home, can I text and call on the Apple Watch?

I really want to buy the Apple Watch SE but i have some questions regarding this device.

If i leave my phone at home and go out to drink some coffee for example, can i still send messages and call people without my phone near me?

The same with music, if im in the gym and i left my phone at home can i still listen to music on Apple Music or Spotify?

[Re-Titled by Moderator]