Hi,
First, you don't need a tax rule for 0% tax, since when no tax rule apply, products won't get any tax added.
So the tax rule with the 0% tax rate can be deleted.
Second, yes, for all the other tax rules, besides the one for Hungary, you want to select "individual" and "company without vat number" in the client type setting so that the tax only apply to them.
Companies with a vat number will automatically see no taxes in that case, unless they are in hungary, where they will pay the normal rate.
Also, beware of the "Type of address used for tax" setting in the HikaShop configuration as the system can use either the shipping or the billing address based on what you select in that setting.