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And here is Matt Cutts talking about multiple redirects: https://www.youtube.com/watch?v=r1lVPrYoBkA

Use the infographic. Seriously. That is what I did to explain the concept to our developer and it worked better than any long-winded descriptions I had tried.

According to your description, http://site.com/oldurl is the link with equity and https://site.com/new is the final destination link. Is this correct? To get from one to the other you go via a 302 and at that point you lose your equity. Whether it is a redirect of a redirect or not.

And in general, multiple redirects should be avoided. Google will follow multiple redirects, but you will lose some authority with each jump, and at some point, maybe more than 3 or so, Google will give up.

If they have no traffic and no links, I would not move them.

I would only re-purpose them if you think that by combining/editing them they would have value, but in a situation like this, that usually isn't the case.

(Unless we are talking about a significantly large percentage of your website becoming 404--in that case some rewriting/repurposing would be in order.)

Yes, using a 302 redirect loses link equity. You can take a look at: http://moz.com/learn/seo/redirection for more information. "A 302 redirect is a temporary redirect. It passes 0% of link juice (ranking power) and, in most cases, should not be used. "
*I also love this infographic: http://moz.com/learn/seo/http-status-codes

Yes, I think Party_Experts is right, that duplicating the date will help the user's experience because they'd be able to see all of the information together. As far as H tags, anything lower than the H1 tag is probably not going to have a lot of influence, so I wouldn't worry about that part too much.

No, rel="canonical" is the same internally or cross-domain. You are just telling Google which copy of that content to serve, wherever it is. (And rel="author" is no longer used by Google to show authorship in results nor is it tracking data from content using that markup. http://searchengineland.com/goodbye-google-authorship-201975 https://plus.google.com/u/0/+JohnMueller/posts/HZf3KDP1Dm8 )

I agree with what Timbronze said, especially about the links. You have very few. And as far as the business name, there are other businesses with the same name, including one with an exact match domain, so there is some competition there as well.

Matt Cutts has said a number of times that invalid HTML in and of itself does not cause a penalty. Here's one example: http://youtu.be/j3KgrbiB1pc

"So Google does not penalize you if you have invalid HTML because there would be a huge number of webpages like that and some people know the rules and then decided to make things a little bit faster or to tweak things here there and so their pages don't validate and there are enough pages they don't validate that we said OK this would actually hurt search quality if we said only the pages that validate are allowed to rank or rank those a little bit higher."

Yes, you should write good HTML. But, unless it is so bad that it causes a bad user experience, simply having some W3C errors is not going to be a problem for SEO. (At least for now...)

Are you asking about a page that has a canonical link which is the same as the URL of the page? That is quite common, and not a problem. (Take a look at the source code of this page--you will see Moz has used a canonical that is the same as the URL.)

Is that exactly how you have the URL written? If so, I think your problem is the missing http://

From webmastercentral:

"Specifying (a relative URL since there’s no “http://”) implies that the desired canonical URL is http://example.com/example.com/cupcake.html even though that is almost certainly not what was intended. In these cases, our algorithms may ignore the specified rel=canonical. Ultimately this means that whatever you had hoped to accomplish with this rel=canonical will not come to fruition."

I have never done it, but Adwords has a policy about it, which makes me think you can do it:

"Links to anchors or fragment identifiers on the same page count as the same page." (from https://support.google.com/adwordspolicy/answer/1054210?hl=en)

*edit
I am referring here to the destination URL, not the display.

Fix the tags and don't worry. As you say, Google will re-crawl and the issue will be resolved.

This is not exactly what you were asking about, but you could look at: http://www.ntopic.org/

You submit a keyword and some content and it will tell you how relevant the content is and also suggest keywords that should (and should not) be there (and how often) in order to improve relevance.

They will have blocks of rooms set aside--it shouldn't be an issue. I have been to conferences in that area and there are plenty of hotel rooms. [I am going too, and also looking forward to it!   ]

You are correct, this has been discussed quite a bit—the answer is subfolder.

Here is an excellent, recent, thread on the subject: http://moz.com/community/q/i-have-a-blog-on-a-sub-domain-would-you-move-it-to-the-rood-domain-in-a-directory

Here is what Rand Fishkin has to say, with an example from moz.com: http://moz.com/community/q/moz-s-official-stance-on-subdomain-vs-subfolder-does-it-need-updating 

An excerpt from his response: "We recently were able to test this using a subdomain on Moz itself (when moving our beginner's guide to SEO from guides.moz.com to the current URL http://moz.com/beginners-guide-to-seo). The results were astounding - rankings rose dramatically across the board for every keyword we tracked to the pages."

Almost all of the information up there is still from 2014. It is still a while before the 2015 conference, they probably don't have everything ready yet.

I keep our privacy policy indexed. I figure that if someone is thinking about interacting with us in some way and doesn't happen to notice the link in the footer or the call-to-action boxes, it should be findable in search so that we don't look like we are hiding something. And for the second part of your question, I think having your privacy policy readily accessible helps users feel more secure and that is a good thing, so I would still have it in the footer.

My CMS is set up such that the title of a page is automatically used for the h1 and the title tag. I usually don't edit this as it is useful to the user--the title of the page summarizes what the content is about. This information is useful in the serps, where you see it in the title tag, and on the page, where you see it in the h1. (You do also see the title tag once you are on the page, but it is kind of in the background, so not really redundant.) I would never use the same content in the h2 as in the h1 just because it would not create a good user experience-- having subsections with the exact same name as the title doesn't help the reader and could be confusing. If your pages are set up around keywords rather than users, then that is probably your problem. As Cole mentioned, consider what is best for the user.

Dashes are Google's preferred word separators. (I have heard that underscores are considered to be word joiners, so in that case your first one would be carfuel rather than car fuel but I am not sure whether that is correct.)

In any case, the two would tend to look the same to your human readers and could cause some confusion there, so if you have the option to change one, I would.