I am interested in getting an Apple Watch Series 3. But I want to know more about how I can listen to music reliably during workouts. I don't want to carry my phone with me. I just want to use the Watch. I would like to be able to store audio (podcasts and music) on the Apple Watch. I may separately have other interests in getting the model that supports Cellular /Mobile service. But I don't want to rely on cell service to stream music. I would much prefer to just store my audio (podcasts and tunes) native to the device (Watch) instead. Thanks.

You can store music on your Apple Watch to use without your phone. To play music you need to have Bluetooth headphones connected - your watch won’t play music without headphones even though it has speakers and does phone calls without them.

Can you use a GPS Apple Watch (no cellular) on wifi to call and text without your iPhone in range?

Yes, provided you have already joined that wifi network with your phone in the past. I’ve left my phone behind and still received iMessages - works well!

Since the price of both the watches is the same, are there any features that normal Apple Watch series 4 has more than Nike + ?

The Nike+ editions come with some unique watch faces and the Nike+ app preinstalled. They also have a few options for bands that aren't immediately available with the other models. Other than that, they are identical.