I'd assume that e-mail etiquette varies considerably across cultures. For example, I have a Japanese co-worker (who has been living in the U.S. for many years) whose e-mails are generally more formal than those of my other colleagues.
If in doubt, it's probably safer to err on the side of formality and politeness.
One thing that struck me about your e-mail to "Dr. Cooper" is that it fails to mention any appreciation of their work or of the time they might spend talking to you. I'd probably write something like:
"I read your paper on foo bar with great interest, and found it relevant to my research on xyz. I have some ideas on how it might be extended to baz. If you're interested and free this week, I'd greatly appreciate it if you could discuss it..."
Maybe also provide a very brief outline on how it could be extended to show that you have some understanding of the topic and aren't just a random person wasting their time.
If in doubt, it's probably safer to err on the side of formality and politeness.
One thing that struck me about your e-mail to "Dr. Cooper" is that it fails to mention any appreciation of their work or of the time they might spend talking to you. I'd probably write something like:
"I read your paper on foo bar with great interest, and found it relevant to my research on xyz. I have some ideas on how it might be extended to baz. If you're interested and free this week, I'd greatly appreciate it if you could discuss it..."
Maybe also provide a very brief outline on how it could be extended to show that you have some understanding of the topic and aren't just a random person wasting their time.