If I buy an Apple Watch series 3

The Cellular Apple Watch shares the iPhone's phone number.  This requires the iPhone cellular carrier to support the Apple Watch.  The iPhone carrier charges a monthly fee for this service.  In the U.S. the fee is $10 per month added to your iPhone bill.

iPhone Cellular Carriers that support the Apple Watch, which models, the radio frequencies each model uses, and the country where they offer service:

https://www.apple.com/watch/cellular

Your carrier Must be listed by name in the above link. NVMO's that piggy back on another carriers network, unless explicitly mentioned, do not support the Apple Watch.

The GPS only Apple Watch can do  Everything  the cellular model can do  as long as  your iPhone is  nearby, where nearby is somewhere in the same 3-4 bedroom home (assuming typical wood frame construction).  And of course when the iPhone is with you when you leave the house.

https://support.apple.com/en-us/HT205547

The Cellular Apple Watch allows you to leave your iPhone at home while you go for a walk, run, bike ride, etc...

The GPS only model will. The cellular function of the GPS+cellular Watch won't work with your carrier.

Yes as long as it has ios13 or higher.

Simple Mobile doesn't support the cellular function of the Watch as I stated earlier.