Does my watch have to paired with my phone?

Yes. Apple Watch requires the pairing to the iPhone to set up.

Once setup, the Watch can be away from the iPhone, and in many cases can be used without the iPhone nearby as long as wifi is available.

For the GPS only model pairing is also necessary to receive messages and calls and as it does so directly from the iPhone.

If the iPhone is not nearby it can use Wifi to connect to the iPhone and still receive calls and messages from it.

See here: How to use your Apple Watch without your iPhone nearby - Apple Support

Yes, always with the GPS model. Also, with the GPS watch you need to have your phone in range, either by blue tooth or WiFi. The cellular model can function without the phone near for certain features but you still want to pair your watch to the your phone. PS Get the watch App if you don't already have it on your phone.

yes, for all of the functions to work.