Apple watch

If you have a GPS only Apple Watch, it is best to just keep your iPhone powered on and nearby, except when going for a walk, run, bike ride, etc…

Use your Apple Watch without your iPhone nearby - Apple Support

Make sure you read the footnotes at the bottom of the article.

The Watch will need to sync activity data to the iphone before it can be saved to iCloud.

It will save a considerable amount on the Watch until that time however Rings and awards may not be achieved if left til after midnight

Wi-Fi connectivity without phone on gps only Watch is quite selective. iMessages and not much else.

I didn't say you could not connect to a mall wi-fi, I said you will not be able to sync workout activity data.

Not familiar with the old Series 3 but I didn't think it had a keyboard for the password.

I would not recommend connecting to an unsecured wi-fi.