In my opinion, you are misinterpreting the definition of a "free market". Surely such a high VAT may have an indirect effect on prices, but the manufacturer's price itself is not subject to control. Compare a farmers market where a uniform admission fee is charged but the sellers still set their own price; it's unregulated.
Also, a percentage tax doesn't really affect competition since it subjects everyone to it - competition on equal terms.
No. VAT is meant to control prices.
If the government would not want to control prices then it would not have VAT or tariffs, it would just have 1 type of tax, and that would be it.
The reason why we got VAT,tariffs, income tax, etc is because they want to control the entire economy. That is not a free economy /free market.
Sorry but your logic fails.