I'm trying to insert div with text to contenteditable and select the text between the div tags after adding the div:
div.innerHTML +='<div id="id">selecttext</div>'
but this won't select the selecttext
<html>
    <head></head>
    <body>
        <div id="contenteditable" contenteditable></div>
        <script>
            var contenteditable = document.getElementById("contenteditable");
            contenteditable.onkeyup = function (e) {
                contenteditable.innerHTML += '<div>Start here</div>';
            }
        </script>
    </body>
</html>
				
                        
Your question has three parts:
Is this what you need?
DEMO