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Those are poor quality pages and poor quality backlinks for your site. Get rid of them.

What steps have you taken to reach out to people and actively obtain links?

Looking at a screenshot of a website is a very poor way to determine content quality.

Might want to add the dev site to Webmaster Tools so you can easily remove any pages that do get indexed.

If Google tells you to do something for better SEO, it's unlikely to produce any significant results short-term. You might get some results if you stay at it for years.

I'm not going to endorse any specific tactics, but if you rely on Google for your SEO advice, you're being fooled. Google DOES NOT want people to be able to manipulate their search engine - why would they give you accurate advice on how to do it?

Adhering to Google's SEO recommendations is your biggest problem. You won't be successful for a long time - if ever - doing that, and don't let people here brainwash you into thinking you will be.

Is it working for them? If so, see if it works for you.

There is no white hat/black hat. There are only differing levels of risk tolerance. And risky SEO does pay off when done correctly.

Attachment doesn't work.

For the future - if you feel like you're getting into a situation where you won't be fully supported to do the best you can, stop and get out.

Check your settings in Screaming Frog for obeying robots.txt, obeying canonicals, etc. That might be your problem.

Link Detox is good for finding toxic links, but you still need to manually review them all. It will give you false positives - no tool is 100% on that stuff.

Rmoov and Pitchbox are good for outreach, though I favor Rmoov since it was specifically built for link removal. Pitchbox is more for prospecting, finding new opportunities, etc.

I'm not surprised, OSE routinely misses many of our links. But none of the backlink checkers will be 100% accurate. Your best bet is to use a variety of sources - OSE, Majestic, AHREFs, etc. - and compile and remove duplicates to get a true picture of your backlinks.

If you're going through with link removal and building a disavow list, you might as well log all the outreach efforts and results - it really doesn't take that long. Just note when you sent emails, when they replied, what they said, and if the link was removed.

I'd upload that to Google Docs and include the link in the disavow file so on the off chance a real person looks into your site, they'll know you did the work.

It's Penguin 2.0, which was put out on May 22, 2013.

Your client can go the easy way with what some would call black hat tactics, rank very well very quickly, get a lot of sales, but then there's always the chance it'll disappear overnight. If you're in to churn and burn and don't care about starting over every few months then go for it.

Or your client can go with what some would call white hat tactics - focus on content, earning links, etc. Results will take a long time to come, but you're better protected from future Google updates. Depending on their resources this may or may not be viable.

Site B likely had a manual action or ran afoul of an algorithm and now that's impacting Site A. Your first step should be to figure out why site B had been going down over time, if it's a Panda issue like you suspect or something else. But don't take action until you know what the problem is.

Moz claims to report the average position that most people will see, but there are tons of factors that go into how SERPs appear for you.

Personally, I find Moz's ranking reports to be reasonably accurate most of the time. Then there are occasions where they report all my keywords dropping out of the top 50 when none of them moved more than 2-3 positions up or down. So take what it says with a grain of salt.

For rank tracking purposes, I use a Chrome incognito window with no history, not logged in, and location set to United States. As long as you're tracking with the same method over time, your results should be pretty reliable.

What steps have you taken to reach out to people and actively obtain links?

OSE doesn't have the resources to crawl as deeply as AHREFs, Majestic, etc., so the index is smaller. Get your backlinks from multiple sources for the best picture.

Using your company name in the title tag isn't (generally) done with the intention of ranking for it. If you can't rank for your brand name, you've got bigger issues to deal with.

Adding the company name to a title tag is more for brand awareness. If people know your brand, it reinforces that they're in the right place. If you're not as well known, it gets that awareness going in the consumer's mind.