Can I show a row of my product page template only on mobile?

Yes. Each row in a template has its own visibility:

1. Open your template under Settings → Appearance (for example Product Templates) and click Edit. Clone a system template first if needed.
2. Click the gear icon (Row settings) on the row.
3. Set Visibility to Mobile only. The other choices are All devices, Desktop only and Hidden.
4. Click Save Layout.

Row settings also include Background, Min Height and Custom Class. Use the device icons in the Live preview panel to check the result at phone size.