何か質問があったら遠慮なく言ってくださいって英語でなんて言うの？

The example you wrote is a good one although you need to put one more comma after "please". In case you want to know how else you can write down the same sentence, I wrote two of them. Basically, they are the same but I personally see the first one as a more preferable option.

In order to make it clear that it is acceptable to ask questions, we should include phrases like 'please do not hesitate', 'I would be happy to answer any questions', 'feel free to contact me' etc. Phrases like this put the recipient at ease and make it clear that it is okay to ask questions and that you are prepared to answer them. Phrases like this are normally placed at the end of an email after another piece of information has been provided. By adding a sentence expressing that questions are okay to ask, we are ensuring that the recipient of the email has understood all the information provided to them and they are free to ask for any clarifications.

Do not hesitate to contact me if you have any questions. "Do not hesitate" is a term native speakers often use. If you hesitate, that means you are not sure yet what/if you want to do something. If you say "do not hesitate", it means that you should not feel reluctant to ask something. In this case, you are saying that the person can contact you no matter what, without having any reluctance. (reluctance means hesitance.) If you have any questions, please feel free to ask. In this sentence, you are also stating that the person can contact you anytime, should they require further information. Should you have any further questions, please let me know. "Should you have any further questions" just means: if the person has any further questions. In this case you are saying that if the person has any questions, they can let you know and you will be happy to help them.

Use the sentences above to express this idea. Assist: help Consult: ask advice from someone Assistance: help Get in touch: make contact Feel free to: be at ease, don't worry about

In a business email, you want to say something like "Please feel free to ask me any questions if you have any". The above suggestions are appropriate for this scenario.