Local optimization - put my real name?

That's really more of a persona l choice but in my experience I have found that it builds more trust between you and your customers if you do that. Plus, it helps you establish a reputation

It all depends on the nature of the business and whether you want your name to be associated with it. Since it's local, I'm assuming you will be personally involved. In that case, using your real name makes sense. As the previous posters said, it builds trust.

Some people do use different aliases for different businesses, but that's usually because it's in a niche that's either very different from their main niche or because they don't want people to know their real name. It can be confusing if people see you associated with a wide range of niches - eg teeth whitening vs. weight loss. That can actually take away from your credibility since it makes it look like you're not an expert in anything.

On the email front, you might want to use separate emails for each business so that you can separate the email you get on each. Just easier to keep them in separate folders and for replying to any email you get on that business.

That is OK. You will look more credible with your real name.

Oh yes, of course! I would strongly suggest that you do otherwise people will think you're a fraud (if ever they found out that you used a different name).

Probably the best is to use your real name for the main business and a pen pal name for something not related to your business. The reason: to build credibility, nobody will take you seriously as expert if involved in totaly different niches. You cannot be "The Jack of all Asses".