How does the person sending the message know it is being sent?

Answer 1

In the cell phone like mine, I get a small window that says Message Sent. It it stays up for about 5 seconds. Most phones will have similar ways too.

Answer 2

The screen will usually show some where on there "sending message" or something similar. If you want to see if it was actually sent check your outbox, messages usually still in your outbox were not sent.