「他に質問があれば、メールでしてください」って英語でなんて言うの？

「他に質問があれば」は "if you have any other questions" と言えます。「メールでしてください」については、①のように "please send me an email" や "please email me"（メールしてください）や、もう少し丁寧に、②のように "please feel free to email me"（お気軽にメールでご連絡ください）と言うことができるでしょう。

ご参考になれば幸いです。

In a business situation, keep your language formal. Include terms such as 'please' and also, follow up with a 'thank you' because this is polite.
The 1st sentence is more friendly and by saying 'please don't hesitate' you are making them feel welcome to email.

These examples are standard closing remarks to a lot of business emails.
The words "feel free" and "do not hesitate" are phrases used to let the person know that you are happy to help them with any additional information that they might need.

"Should you have any further questions, then please do not hesitate to contact me".

"Please feel free to contact me should you need any further assistance".

To "inquire" about something, means to ask questions about something. We usually say "don't hesitate to" when we mean that you should not be scared/shy to do something, in this case, don't be scared to ask questions via email. "Feel free" means almost the same as "don't hesitate". It carries connotations of being able to do something without any reserves. Hope this helps! Thank you for your questions.

If you are in a business situation and want to tell someone that they can email you if they have any further questions, you can say something like "Should you have any further questions, feel free to email them to me.". By using phrases like "feel free" or "do not hesitate", it makes the conversation sound a lot more relaxed and like you will be very welcoming towards any questions your client may want to ask you in the future.

The above sentences are common ways of explaining to colleagues or clients to contact you should they have any questions on a topic or project etc.
Drop me an email/ reach me by email are typical phrases when talking about sending or receiving emails. It is common to hear people using these in the office.

When concluding a business interaction or meeting it is common to ask if there are any further questions or to advise of your availability to answer any future questions.
You can specify how you wish to receive those questions by saying a general 'don't hesitate to contact me if you have any questions.' (leaving the method of contact to be decided by the client.) or you can specify if you will accept a phone call (feel free to call me if you have any questions) or if you want written/email contact, such as:
- Feel free to email me any questions that you have.
- Please put any questions you have in an email to me.
- If you have any questions, please email me.

It is normal for us to have doubts after having a meeting with someone. It may be the first time we have had a meeting with this person, so maybe we have lots of things to ask but don't remember everything. Sending the questions in an email is a great way to confirm any of our doubts.
A "query" or "queries" in plural, is another word for questions or doubts.

Using this sentence is a polite and a very formal way to let the other person know that they can contact you by email if they want to ask you any more questions. This would be a good sentence to use in formal/business situations.

Situations where this word/phrase is used: social, business, formal, when asking someone to request extra information if necessary.
Type of word/phrase: standard language/business language
Example of this word/phrase:
"Further to our telephone conversation earlier today, if you should have any queries, please don't hesitate to email me."

If you are in a meeting, and you would like to let the people know that they can ask any follow up questions through email, you have these two sentences.

For example.
So, that concludes are meeting. If you have any questions, please don't hesitate to send me an email. Great. So, if that is all for today, I will see you soon. Have a great day.

I hope this helps.
Have a great day.
Will.