Hello David,
I replicated your example in two ways. First by adding the code via my Netobjects web tool and second by generating a html file identical to yours but with my own cloudlink pasted in. The results are different compared to yours.
In both setups the manipulate appears nicely in a firefox or chrome browser. For unclear reasons the cloud wolfram object appears in the IE browser but not the manipulate object.
I've tried to trigger a timeout message. After 10 minutes of inactivity this does not happen.
The really strange thing is that it also does not happen with your original html code. I only pasted in my cloud object.
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8" />
<title>Test CloudDeploy Manipulate Embedding</title>
</head>
<body>
<h2>A Start</h2>
<p>This is a bit of text before the embedding code. </p>
<iframe src="https://www.wolframcloud.com/objects/YOUR_OWN_GENERATED_ID?_embed=iframe" width="500" height="500" > </iframe>
<p>And following is this bit of text.</p>
</body>
</html>
All browsers are on the latest versions and on windows 7 64.
About the wolfram branding. No idea how to get rid of this. No other programming language does it this way. Lets ask WL support.