I am sending iMessage to other iMessage users and sometimes it’s Green and sometimes blue depending on the person. This happened after I got the iPhone 13 and transferred my info. I can’t get it back to blue for iPhone users.

If you checked Settings>Messages and iMessage shows that it is activated and your Send & Receive shows your Apple ID and Phone number, then he would need to check the same thing on his device. So if this happens when you are together, that would indicate you are both connected to the internet. Does it happen when you are not together so you are unaware of his type of connection?

I went into my settings. To receive iMessages my cell number and both my email numbers are checked. To start a new conversation my cell number is checked. However, some of my iMessages are being automatically erased to some persons who have iPhones. What should I do?

iMessages changing to sending by SMS can happen for a number of reasons. This can happen usually if either one or both of the people involved lose internet service for any reason. It could be a loss of cellular service if away from home, or wi-fi issues. However, you would be best to verify that your iMessage activated properly. Go to Settings>Messages, and make sure it is. Then you can check what is set for Send & Receive. If one of them sends you a message and you respond, does it send as an iMessage? Are you also sure these users still have iOS devices?

My wife and I had the same problem after getting new phones. My messaging settings was not using my phone number; it was sending and receiving via my email. The number was listed but unchecked. FWIW, my carrier botched the first attempt to activate my phone. Choosing my phone number solved our problem.