Please don't be shy, feel free to ask questions if you have any.

To hesitate means to be uncertain to act, to think over many times before acting. The expression "don't hesitate to" is mostly used in formal letters and politely encourages the other person to act easily and with no doubt. E.g. "If you need more information about our company, please, don't hesitate to contact me".

It means 'feel free to...'. It is a polite way of saying that you are welcome to do something. It is quite formal.