I would advise against using multiple H1 tags on the page. Instead, Oleg's approach could work.

Just replicate it as you wish and use CSS to make it look the same.

Of course, doing this across every page on your site may seem a little spammy.

Since your emails are not indexed by Google, no.

Of course, as a general business practice, what to include in your signature is up for discussion. It can certainly generate traffic. Google claims not to pay attention to Google Analytics data including traffic sources etc. so it is unlikely to have any benefit other than the direct traffic from the person visiting your site.

Sure. I thought you were just repeating the titles for the sake of repeating them.

The general SEO community consensus is that you should:

A. be doing what is best for the user (so not concealing the H1 tag)

B. not doing anything that could make Matt Cutts and the Google team upset

They have advised against attempting to conceal content for SEO gain so I would strongly recommend avoiding it. They have been dealing with these issues now for a LONG time, so presumably their bots can easily pick up on those tricks.

The Google bots can now "see" what is visible on the page. They discount things that are not in the visible content area so the benefit to an offset H1 would likely be none. Also: They're watching you.