So I can edit/create invoices to show price without VAT, how much is that VAT in %, how much is VAT in cash, and then total price together at every line of a bought product [..] in Free plugin?
Yes, with a custom template (instructions here) you can read this data from the $order
object and print all data that is stored by WooCommerce. This does require a modest level of PHP knowledge.
like it’s needed in most of EU countries
The default output shows the total amount of tax per rate in the totals, which is sufficient for most EU countries.