I'd recommend you do neither.

If you set them to no-index, these issues won't matter, but you won't have lost the pages and whatever value they pose. Plus, it's generally good to keep any pages that aren't of their own accord, detrimental.

However, if you'd rather not do this, I'd look more favorably on removing them than fixing each one. That's a lot of work for very little reward - most likely, at least. Really, the answer depends on how much time you have and how fixing them would weight against the benefit(s) of doing other things.

Yes, the word "in" would separate the keyword, though you technically would still get a reasonable amount of worth from the phrase in general. Some longtail keywords are incredibly difficult to get into content - it may be worthwhile to try to find ones that are high-volume and less abstract.

If your client is adamantly opposed to having the better of the two consume the other business, then yes - the only other viable option I'd see would be to treat them as completely separate businesses that are only related by owner. Name, address(es), phone number(s), email(s), etc. should all be changed if that's the case. For all intents and purposes, they would have to be treated as two unrelated businesses.

I hope your client will chose the prior solution rather than this, but I imagine either would be better than continuing in their current state. Good luck to you.

I would strongly recommend removing the one that's not doing well locally and adding the content to the structure and content of the other website. Your client should also consider condensing the two businesses into one.

I say that because from what you said, it sounds like he views the two service types as different businesses that only share a name. This is very likely counterproductive, and I'd have to assume means that both websites are competing against one another in SERPs regarding branded keywords.

Touting all of his services as one business would have a lot of different benefits; but is there any reason he's treated them as separate businesses? If so, my advice may not be prudent - but it seems unlikely that there's a good reason to do so.

I would add that there's is no text on any of those three pages - any "text" one would see there is actually just embedded in an image - which is a huge issue for a number of reasons:

1. Search engines see that there's no text - a big no-no.
2. You're getting practically no SEO value from the content that would be there, even if there isn't much.
3. It's heavier this way - which makes load times slower.

I want to clarify that there are many, bigger issues with these pages - but as your question concerns only duplicate content, I'll leave all of that out for the time being. To summarize, Google, Yahoo, and Bing are just seeing some duplicate banners, sidebars, etc. and then some images in the body of your pages. Hence, duplicate content.

First, an H1 should pretty much never be in the footer. H1 tags are meant to be the lead-in for the page and the content therein. It should tell visitors and Google what your page is about, using keywords if possible. That said, there isn't inherently anything wrong with having 2 or 3 H1 tags if your page is long and has several different bits of content that don't fall under one category.

Second, while it's important for a company's name and brand to be relatively prominent on a website, having it on every page as an H1 tag is extremely excessive. If I saw it as a user, I'd think it's not only spammy, but strange since it's presumably in other prominent places on the site (in the header, content, some H tags, etc).

I strongly recommend that you remove these H1 tags from your footer and, if having the brand name within pages is something your client really wants, have it placed more organically in the content.