Price not updating on custom theme template
What you've heard is correct: Drupal Commerce adds classes around product fields that allow the Add to Cart form to target those rendered fields for replacement when attributes are selected. This is why in their absence you won't see prices updated at all.

The simplest way to illustrate it will be to simply look at the HTML on a site with a working theme and your custom theme to see what those classes look like.

The classes exist in the render arrays for these fields, so you simply need to ensure your theme is properly including the HTML element attributes for these rendered fields. Again, for that I'd simply advise you to look at working theme code to see how it's done elsewhere.