A page per service area is likely to be better from a pure SEO perspective, particularly if these relate to phrases that potential customers are likely to serve.  A page per service is going to give you the opportunity to really expand on the information on offer and probably rank for more related terms further down the tail as well. It also makes is easier to focus your one page optimisation more at the theme for each page.

From a user experience / conversion perspective it could help too.  That additional information, some focus and the chance to sell the benefits more should funnel more people towards conversion if it is done well.

One potential pitfall is if you are in an area where potential customers might not know exactly which product areas are right for them.  The "everything on one page" approach can work well when people want to scan their eye down what is on offer and find what is relevant to them.   Many sites now take a best-of-both approach: Have one page per service, but still have a services page that gives a shorter overview of each aimed at directing people towards the right choice for them, as you suggest in your last paragraph.

Both are quite different, so it really depends on what you are after.  I'm actually a big fan of majestiseo (just to confuse things further).  OSE is good for understanding the big picture. However I find that its crawl isn't anywhere deep enough for the stuff I work on - particularly in terms of deep pages on large authority sites.  Example:  links from the bbc are almost the holy grail for some of the projects that I work on, but OSE often misses them.

Ahrefs is better, and majestic goes deeper still. The down-side of that is that you get a lot more low quality stuff to sort through.

In terms of majestic v ahrefs, ahrefs definitely wins in terms of interface / tools.  I'm an excel guy though, so it is all about the data for me - hence majestic being my "weapon of choice".

Why not check for yourself?  Same logic.  Put image URL in to image search, but this time add site:pinterest.com to the end.

http://goo.gl/OGgeb8

Not thousands, but there are some.  You can now check the source of those page to see whether there are followed links or not.

No problem.  This isn't the clearest example of what I am talking about, but it was the one that I had open in a tab when I got the email notification of your question!

http://www.backcountry.com/3-season-tents

The top of that page has three guides.  There are three more at the bottom.  Those guides are in a place where customers are more likely to see/use them. That makes sense as they are also great sales tools. Those that open in a modal window for that page also mean that the category page becomes the page that attracts links rather than the blog page.

If you put the URL of that image in to Google's search by image you get this list of results of where else that has been us3ed http://goo.gl/mkAdJW

If you go down that list you will find that the majority of those sites then link back to the originating site by way of a credit.  Voila - links!

So the process there was most likely to produce a list of sites that might use the infographic and contact them all to offer it (requesting a link by way of credit).  It's an effective method in terms of the number of links that can be generated from it, but it doesn't create the best overall link profile.  A lot of the links can be from pages that drop off quickly or from sites that link out to almost anything.  It also creates a very definite pattern.  Not to be overdone, but it does still seem to work.

Your structure is probably the most common.  As you say though, you do risk cannibalising your own results.  You could no-index the blog categories.

My preferred approach is to have blog and store more closely integrated.  This can allow you to do away with blog category pages entirely, and have those as part of the e-commerce category. Bringing the content closer to the products brings a number of benefits in terms of both SEO and Conversions.  It also results in much richer category pages which can be another big win.

If you have a full list of URLs you could check for cache date on each at Google.  Unless you were doing that manually it would be technically against google TOS, but so is SERP checking.  More to the point I don't think it would be foolproof as indexed pages will sometimes return no cache date.

It's a bit of a convoluted method, but I think that might be your only option.

The answer to this depends on what you are trying to achieve with the video.  Video can serve numerous purposes in online marketing and the best methods to employ differ a bit depending on what you are trying to achieve.

If the aim is for as many people as possible to see the video then you want to include it (or a version of it) on YouTube. YouTube is in itself the second biggest search engine on the internet, so a properly optimised video there has the potential to be seen by a huge audience.  This is perfect for video that, for instance, introduce your product or service as a solution to a common problem.

One use of video that we employ is to obtain rich snippets.  A video rich snippet can leapfrog your page above others in the SERPs and also bring an improved click through rate. Win!  If your video is hosted on YouTube and embedded on your site then this is not going to help you.  The reason for that is that the rich snippet will lead to a youtube page, not yours so you want to host it privately.

Privately doesn't have to mean on your own server. In fact, in most cases we avoid that.  Services like Wistia and Vimeo have paid options that allow you to upload your video with all the ease of youtube, but control which sites the video cam be embedded on. This protects your video and helps you keep that rich snippet result to yourself.

We often now look at using Wistia/Vimeo for the main video, but doing a second edit for YouTube if the content suits their audience.

As Dana says, Phil Nottingham has put out some very good posts about this, and also how to get the most out of whichever path you go down.  There is an outfit called reelseo who have also done some good posts on this.