Mark Fortune

It is very possible that there is a new version of the Google Play Store available. If that is the case, open the settings menu in the Google Play Store app, scroll all the way down, and tap on the Build Version section. That should tell you if it is up-to-date. Also, try restarting the phone. And are you using Wi-Fi, or a cell connection to download the apps? Hope this helps!

Yes, there is a WiFi antenna inside the LG G Watch R, however WiFi functionality was only recently added to the G Watch R in a more recent update via Android Wear.