The developer choses a pricing tier, and then Apple sets the prices for all countries. For example, the developer may chose a pricing tier where the app costs $9.99 in the USA, and then all the other prices are set automatically. The price takes into account the different currencies and taxes that need to be included, and then the price is rounded. Some prices are rounded up, some are rounded down.
One Apple ID connects you to _one_ country's app store. Buying from two different countries means two Apple IDs which is a permanent pain in the ****.
No, different country has a different price on the same apps, because of different currencies, taxes, and exchange rate. But it is generally similar. If you want to login different country's App Store, you should prepare different Apple IDs.