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Does the central bank directly control the interest rates that are important for consumers and investors? How does the central bank influence the interest rates?

Answer ,No, the central bank directly controls only the interest rate at which it lends to commercial banks and the interest rate at which commercial banks can deposit their excess reserves in an account at the central bank (typically overnight). The interbank rate will then lie in-between the two interest rates picked by the central bank

In addition, the central bank performs open market operations by buying and selling government bonds or by entering repo agreements, and sets reserve requirements for commercial banks.

All these operations feed into the interbank interest rate, which then is reflected in the interest rates that are relevant for consumption and investment decisions.