Text message from non iPhones

Is the sender of these messages using your mail address to send the messages to your phone?

As long as they use your phone number, it should work.

Also check this article again:

If you can't send or receive messages on your iPhone, iPad, or iPod touch - Apple Support

Is this only one particular Android user, that can not send you messages, when you have switched on iMessage?

Does it work, if you are not connected to Wi-Fi, and using the cellular network?

Since messaging is also related to the carrier, did you try to contact the carrier about that?