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And why exactly would you redirect a working (well aged) domain with rankings to an entirely new domain with a .mobi suffix and no rankings? Just for the extra related keyword in the domain?

Don't do it then. You're making a big sacrifice for nothing. In my experience, .mobi domains don't have that much value as .com domains (no hard proof of this). The new domain also has some issues apparently. I won't start from zero on this one.

Another thing: don't trust one tool when having a lot of bad links. removeem.com is only one source where you can find your links.

+1. You should at least earn some links, not only building. It will get easier to build links with real valuable content.

You can use the disavow link tool. Get a scan where all those links come from and paste it there. Google will see eventually that the domain is spammy.

You can check search engine usage with statcounter:

http://gs.statcounter.com/#search_engine-RU-monthly-201206-201305

The ways to get included? Having Russian specific content is a good start. And links from that area. And a sitemap. Use Google and Yandex webmaster tools.

Most of these links have a nofollow link, so it doesn't really matter. You won't get penalized with a nofollow link.

It's better to put your linkbuilding effort in other channels than these low value directories.

Right now there are still 96.000 results in the google index, I guess it's taking a while before their crawler crawls all of them. It's a matter of time before they all will be moz.com results.

There's no relevance nor context for these links. It's linkbuilding instead of link earning, so I wouldn't do it.

In my opinion, it's a gift when they want to scrape you. You have copyright on anything that you have written. When I got scraped, I file a complaint trough the DMCA form. Their results will get banned from the search engines in a few days.

If you've set your links and your author right, you don't really need to worry: you're doing everything you can.

Short answer: no. Parked domains are so different that you can't really make anything to check it. Some have a header 302, some have 'want to buy this domain?', some have only ads. It has endless variations and there's no standard.

Case A:
If the content of the PDF's is valuable, if it contains also some text about the product, I would make them indexable. It will make niche searchers find you.
You might want to make a separate sitemap for these PDF's, just to keep things clean.

Case B:
If it's only numbers and very technical jibber jabber, I wouldn't let it index, since Google won't understand it either.

Update with an interesting story:
A client of mine also had technical PDF sheets online. He has put a lot of effort in that. There were a few (4-5) competitors using direct links to the PDF's. After a while, we referred all that competitor traffic to a special landing page trying to convince why my client is a better deal. It's still online on some of the sites, since some competitors never really checked the PDF's.
Made my client very happy.

It's a factor, but not the only one. I wouldn't mind: it's already a win that you can create extra authority from the old domain.
In short term, it's more interesting to keep the old domain name. In the long term it's more interesting to have the new more relevant one, kickstarted with (301) links from the old one.

It's a preference, there's no right or wrong here. If going for the long term, relevance is my number one choice. You should see the old domain as a gift to kickstart it.

Depends. If your domain name isn't that relevant for you business, I would buy the new domain name and do a 301 redirect. That way you can still profit from the authority of the old domain name. You won't get everything, but it will still kickstart your new domain.

Relevance is everything. You don't want to change domain names later on.