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If using straight AdWords retargeting is out of question, I would recommend looking into DataXu or Media Math. Both have been good partners for me in the past. I would stay away from AdRoll or other similar partners that primarily use Facebook for retargeting for your situation. If possible, use dynamic retargeting to deploy the most relevant ads to the users.
Did you make any other changes (targeting, etc) that would have caused these increases?
Based on what you've shared so far, the additional budget has increased visibility volume, but the quality of audience has either dropped or are experiencing ad fatigue. I would look at lowering the number of impressions first. Then I would raise your CPM for each, but at a % that's appropriate for each ad group (they perform differently and should be treated differently) to see if it offsets the CPC raise.
Take anything Google says with a grain of salt and look at the UK as a whole for general search behavior. That will give you a more accurate read of search volume & behavior, then take what you've learned and apply it through a local lens where necessary.
For example: search phrases and behaviors for floral shops may be different in the UK as a whole than in Tunbridge Wells because people on a local level could be using mostly branded terms and looking for directions. I would complete several local business citations & profiles and use general search terms for the website.
I have finally given in to feedly. It was much easier for me to make the transition than I had anticipated. After two weeks, I was glad I switched.
Why fix it if it isn't broken?
Meaning, why do you want to remove the redirects? I see little benefit from serving a 404 page in stead of redirecting to a better suited landing page.
Based on what you said in your question, you won't be able to see any Search info unless the user has recently visited the site through search and then returned via email. You might be able to drill down to this in Analytics by digging into the conversion paths. If you're just looking at email, you will obviously not have Search terms associated with the user. If you are asking about the email acquisition from the ad extension, then you'll be able to pull the search term by drilling into things in AdWords.
More info from you would be helpful in answering your question.
No negative impact. Unless it's a one service/product website, the heading "Overview" would not be the best use of the tag. This would be something more like "Real Estate Refinancing Product Overview" or something much more descriptive of what is to follow.
Utilization of H2's and H3's will also be useful towards structuring the overview page.
Duplication would be my secondary concern. After running many site audits this year, I have seen how many sites have duplicated heading tags as a result of how it was built into the site theme/design. My recommendation is to make h1's an editable field at the page level, rather than generate automatically, or, style it remove the tag from page heading's (as you suggested), this would be the next best option.
We have seen constant churn on our major brand name KW rankings for quite awhile. Nothing as major as November 2012, but we never get too comfortable in our position. We constantly keep doing what we have done in the past, building out our network of authorities, securing links from vendors, building advocates, good content and making sure our site is very attractive to the crawler 
Was there an increase in "not provided" that would justify the drop in branded traffic? That can happen.
First, isolate the cause. Did you check seasonality as well? Is this a pattern or can it be attributed to more data gobbled up by not provided?
I would doubt any penalty would result in decreased rankings over branded queries only. If your non-branded traffic was still solid, I would keep digging in Analytics for the answer, unless the brand name is exact match for the query..
My questions are:
1. Do apps help generate more likes?
Not necessarily. Plenty of companies have custom apps that fall flat on their face. Volume is always key. Sure, if you have clients that have visibility, a nicely thought out app will drive more likes. Heck, just using a fan gate alone. A lot of companies have their hat in the ring now, it's about looking at being unique and very usable. Usability is a big part of the equation with building and maintaining apps. For instance, tabbed apps no longer work in mobile.. which may account for a large part of your user base.
2. Can Apps be promoted?
Yes. Are speaking of promoting indirectly or directly? Suggest reading: https://developers.facebook.com/docs/tutorials/mobile-app-ads/
3. Is it challenging to create a Facebook app?
A good one, yes. Don't build it simply to compete, fill a open desire in the marketplace. Maintaining an app is also something to consider. I would firstly assess your budget, then look at what you want the app to do. Talk to potential customers and see if it is something they would actually find a value in.
4. Are Facebook apps worth investment of time?
No crystal ball here 
Sure. Since the search still shows you all results.. simply does not give you the number.. what you could do is go ahead and paste the code into text editor or Excel, then filter by a pattern with the image links displayed. Pulled the total count that way. Yeah, it's a bit more work BUT at least they aren't using pagination
For your reference:
The general thought is that they will take up valuable ranking landscape, since your title lengths are limited to begin with.
Glad I could help!
Here are some good sources to get your feet wet:
I know this question has been asked here a couple of times in the past.. but does anyone have any insights on when the Search Engine Ranking study will be released this year?
2011- June 8-9th
2009 - August 23rd
2007 - April 3rd
If history tells us anything, we should be looking at this month or next at the latest! Search Metrics and Chitka both recently had noteworthy studies released in the organic search landscape.. so I'm expecting something big!
External factors play a big part in this. If you aren't carrying a site like Amazon.com to use for your linking disposal, you're going to have a big uphill battle. Unfortunately, right now, part of that battle is the quantity of Time and significant natural growth within your link profile. Sites like Diapers.com can become a major competitor quickly (and you'll see this with Media groups & corporate conglomerates as well) as they have the whole network of sites at their disposal. Linking schemes between the properties can bring these relatively new players hundreds of thousands of dollars in organic traffic revenue in a relatively short period of time.
Your specific scenario is a tough one to speculate on.. simply because we can not see what you are seeing without looking at the sites in question.
First off, sorry that you're running into ranking problems. It's never fun, but always turns into a learning process.
Upon inspection, it seems as though your link profile is lacking a set of links with integrity. Those that come from natural evolution of the lifespan of a linkworthy site. Looking at your link profile, sorting by external links to the root domain shows top links are from directories in large part. Granted, they are directory links with good authority, I would surmise that there are a lot of competitor links you could obtain as well as the ever-sought-after editorial-type links.
You're right. Big brands have these and they will continue to grow in SERP saturation within your vertical. The best thing you can do is be dynamic, target time-sensitive news items, provide better content and build your network of bloggers, social authorities, youtube users and grow your footrpint the right way.
Look to the link profiles my friend.
Yep, you're going to want to avoid the strategy altogether unless the infographic is extremely useful and proves to make a splash with users.
Share with like-minded power users on Social Media, reach out to powerful bloggers within your niche and talk to friends to get the word out. Also, Visua.ly is your friend.
Don't waste time going after sites like Ezine Articles or the like.. even one submission at a time.
It really depends on the types, quality and anchor text saturation in your profile. Anyone who says otherwise is just plum crazy. It's impossible for anyone to say without looking at the link profile in question.
I agree with Todd unless you have a good recommendations engine. If that's the case, related or suggested products would still provide value to the user even if the product is no longer attainable.