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Google addresses it here.

No way to change it. They feel that their title is more relevant toward the searcher's query than yours.

Don't use them. The major search engines do not use them and by not using them, you have less code which will ultimately reduce server processing time (incrementally matters in volume).

Are the links for SEO purposes or for users? If they are for SEO purposes alone, I would get rid of them (always focus on your prospects).  Like Takeshi said, if you watch your data, it will guide you into what you should do.

Noticed this as well--especially for some long-tails that we were ranking extremely high for steadily dropped to the bottom of the page and were taken over by sites with extremely high DA.

IMHO, Google probably steadily increased the weight of the DA factor and this caused a shift in the organic rankings.

Yeah, give us the url. Could be a wide-range of things including: robots.txt file, directory was renamed, mistake you made in webmaster's tool and so on.

Why do they want to keep it? Implementing 301 redirects is essential and is the best-practice as you want to have only unique content out there.

Yes, shouldn't be an issue. However, you can check image meta data through http://metapicz.com.

I am not sure you can batch these up.

I believe it probably does (although probably not a significant amount). As the size of a site increases (with unique content), it may be easier to gain trust and authority. However, quality of content/inbounds links still would heavily drive rankings.

It's difficult to tell. If the kw's you are trying to improve rank for are fairly competitive, 3 months is a short amount of time.

Agreed. Always do what is best for the user. Sometime people stuff their title tags to get most "bang for the buck" and often times this can hurt them. I always look at the title as a cta in the organics and try to make them compelling and unique and don't care that much about min. length.

Good find. Here is the link.

Organics around 15% and PPC about the same. Rough average comparing monthly totals average out compared to the summer months.

The url's may be blocked for indexing, but if they were indexed at one time there is a lag time before they are typically removed from the organics. Is this is what you were asking?

The SEO process is never complete, but always a work in progress. Just give it some time and work in getting some good contextually relevant inbound links.

Useless? Everyone knows this information? IMHO, I thought it was well put together and useful...

I know that there is a thumbnail meta tag:  --but I doubt this populates it. My gut tells me that Google will do this automatically.

On seorountable, they speculate it may come from product schema/market and the rich snippets Google shows for them.

If no pages are related, I typically take them to a customized 404 page. You don't need to remove it from GWT:

When a page is updated or removed, it will automatically fall out of our search results. You don’t need to do anything to make this happen.

This actually happens quite a bit and specifically for long-tails.

The key is to be passionate about SEO. If you are not, find someone who is. Read the blogs/forums, watch the videos, track and change things. Make a daily effort to spend 15-30 minutes on moz, webmasterworld and other seo sites and over time, you will be up to speed. Good luck!