Does an Apple Watch need to have a cellular plan of its own in order to text or call

No. Apple Watch can make calls/send messages so long as your paired iPhone is within Bluetooth range, or it's connected to wifi.

For it to connect automatically, yes. Depending on the network type, you can manually connect to wifi networks on the Watch itself.

Doesn't it need to be a wifi network that the iPhone has previously been connected to?

M1 Mac mini, macOS 11.0.1; Watch, series 5 GPS/cellular, watchOS 7.1; iPad Pro 2nd Gen, iPadOS 14.2; iPad Air 2, iPadOS 14.2; iPhone 12 Pro, iOS 14.2.1; TV 4th Gen, tvOS 14.2  HomePods, audioOS 14.1 and Airport Express w/ Airplay 2