How can I send a message to another Ethereum address? And how would that user receiving know that its a message? Is there an Ethereum wallet that will show that I sent a message to that address? And what is the max size I can send?
ethereume is not social media or any platform to contacting.
Only way to send msg is send msg as data by myetherwallet or some other method, he can check your msg by read input way in TX.
Ethereum itself does not provide a messaging service. But it provides an infrastructure that allows to build such applications, such as Toshi (formerly token) and Ethychat, for example. The notification of user depends, although it probably requires some external and most likely centralized part, since Ethereum does not provide a native support for that. Also the maximum length of the message depends on the application.
Additionally, Ethereum has Whisper, which is a protocol for secure messaging between DApps. This protocol seems to be the proper way to implement messaging on top of Ethereum, even though it does not seem to be used widespread.