Asking a faculty member at my university that I have not met(!) about his research, and about courses that deal with his specialty/my career goal?
It is completely fine to send an email. Your request is totally reasonable. You are a student, at university to learn. The professor is at university to teach. If they get offended by a simple enquiry that shows interest in learning more about their favourite subject then you have a bigger problem on your hands.
It will not be the first or even the hundredth time this professor has received an email from a student they don't know and writing such an email is not going to cause offence in any way, shape or form. The worst that can happen is you get a polite &quot;Sorry, I am too busy&quot; or perhaps no reply. The professor will not be offended by you asking -- in fact, it's more likely they will be annoyed or frustrated that they don't have the time to help you, not at you for asking.
Finally, I would not start off with such a grovelling/self-deprecating tone. There's no need to apologise for sending a perfectly innocuous email. However, please bear in mind that academic cultures do differ, and I'm writing from a UK/Western European perspective, where the culture can be a little more blunt and far less deferential towards authority (i.e. professors) than in the USA (where I assume you are from). To me it would come across as more professional if you write to them as though you are a peer wanting to initiate a scientific discussion, rather than as a lowly student who isn't worthy to interact with an esteemed professor.
In summary, the best thing to do is make sure your email is short, polite and to the point. Briefly introduce yourself, ask your question and thank them in advance for their time.