What language is the code of the embedded survey?

The short answer is yes, it will help your whole site.

As for the long answer:

Every page that is included in the structure of your website, has internal links pointing to it, or has external links pointing at it will have some amount of authority/page rank.  Of that authority, a page is able to pass 85+% of it's total authority on to other pages.  So, if you have 10 links on that page it will pass around 8.5% of its total authority on to other pages.

So, let's say you have a blog post about the "50 Best Logos Ever." From there you would want to link back to your logo service to try drive authority back to those pages.  That way if your post gets links you will be able to drive more authority back to your pages that make you money.

Unfortunately, quality back links aren't going to come from a list.  The best kind are naturally earned with great content, but you can supplement this process with a great guest blogging process.  To do this you will want to find blogs in your niche, which would be anything about advertising really, and build a relationship with them so that they will accept your guest blog posts.  There's awesome resources out there for best initial emails to start this process, but I don't have any saved off hand.

The ideal option is actually getting links naturally.  To do this you will want to great engaging content that gets people to link to you.  This may be a list of the best 50 logos ever, or 10 reasons why you need a virtual assistant.  Anything that will get people to read it, comment, and then blog about it.

Depends on how cute the cat is.

I agree with Tom on this point.  I'd create a short snippet, and just link back to the original article.  That way the traffic still flows through you, in case you have Ads on your site.

The only exemption to this for me would be if the content would be so amazing for my community of followers.  In that case I might accept the content, and just no-indexing it.  That way people in your RSS feeds can get it, and not have to jump over to another site, but you won't run into issues with Google.

"If I suggest that they make an H2 tag with SEO..."

H1's carry a little more weight than H2's, so I'd suggest using an H1 if you can.  Ian implied that, but he didn't outright say it

Also, the page you have listed has capital letters in it, which isn't ideal, but it's still fine.  However, the lower case version does 404.  So, any links that are sent to the lower case version will not result in you getting link juice to the page.  I'd suggest using a 301 redirect from the lower case version to the upper case one that you have listed.

lower case version:

http://lightsigns.com/uniko_manufacturing_limited.html

The main intent with the footer link is to try acquire additional clients, so just having it in a blog post can potentially cost you business.  However, you do have to worry about over-optimizing yourself due to all the links with exact match anchor text.  There was actually a different blog post about this recently:

http://searchenginewatch.com/article/2239260/Using-Footer-Links-to-Diversify-Your-Backlink-Profile

In the article it suggested creating a page on your website specifically about this project.  This ensures that you link to a relevant page, in Google's eyes, as well as a relevant page for anyone that is interested in your services.  The blog also suggests no-following all of the links minus the one on the home page.  That way you still get a decent amount of link juice, but don't have to worry about a site-wide link.