When buying 10 lots of EUR/USD with a leverage of 1:100, the price of one point equals 100. Why does the price of one point for buying 10 lots of EUR/USD with a leverage of 1:200 still equal 100 rather than 200?

The leverage set upon registration of the account affects the margin, not the price of a pip, which is the same when buying the same number of lots at different leverages, i.e. the cost of a pip depends directly on the amount you buy or sell. The leverage is needed more to reduce the margin amount — the greater the leverage, the lower the margin, i.e. the more lots you can open.