Hey,
I switched now to protostar to prove that the issue is not produced by template. It happens also in protostar.
I attach 3 screenshots:
1) products-prices.jpg - you can see that all published products that are buyable have prices
2) checkout.jpg - you can see that after a product is added to a cart, it loses the price and the title of the product is modified
3) product-unpublished.jpg - you can see that I unpublished one product, whose title appears in screenshot 3
I can give you access to my Joomla, if that will be helpful
Thanks