Is the Training Plans option to download plans to a device not available on the app version of Connect?

I believe you need the Training Peaks Connect iQ app installed on your device.  Then TP plans will sync to the Garmin device.

No, training plans work also on devices without iQ. I use one for example on Garmin Instinct (no iQ): You do not download it. You upload it to the device from the Garmin Connect Web, using the USB cable and Garmin Express.

Thanks for the reply, trux. My problem is that I only have a phone, no laptop so can't use cable

Thanks Tahoetexan. Will look into Training Peaks. 

1. Managed to figure it out, using the web version rather than the app.