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I think the description and alt tags may count towards the keyword count/distribution, but google ignores the keywords tag for most search purposes.

Links like that don't hurt you, but they probably aren't doing you any good either. I wouldn't worry too much about them.

The types of links I would be worried about are ones that come from foreign sites, pharmacies, free poker sites, etc. that are obviously spam sites.

Were you building inbound links to those pages?

If it was only down for a few days, it's likely that you won't lose any of the inbound links. If the links are still down you should probably create 301 redirects so that visitors don't hit a 404 page.

If there weren't any inbound links to those pages then you should be okay link-wise.

Is there a reason you have 25 different pages? Could you consolidate everything into one page or does each page offer a separate download item?

If they are different tasks, they should have different titles. If they are the same, then there should probably only be one page.

What is the size of a retargeting pixel and who places it on the site ? Is it the retargeting company ? Can we place it ourselves ?  Does a code have to be added to the site ?

The retargeting pixel is simply a way to record a cookie to the users computer. When you setup the retargeting campaign either through google or some other method, you should be given a code to add to your site.

What do you mean by burn pixel ?

When a user converts and you no longer wish to target them, you can send another pixel (cookie) to identify which users have already converted, somewhat disabling the previous cookie.

How do we come to know that a burn pixel has fired ?

The burn pixel is placed on the users computer in the same way that the original pixel was placed, they load the screen with the page with the "burn pixel" and it's stored on their computer.

I think that the number of links you're gaining might cause a problem, not to mention the quality of those links. Google assumes a natural pattern in link acquisition, so when you suddenly jump from 5 links per week to 500, that triggers a red flag because it doesn't appear natural.

How many hours are you spending on this link directory? Perhaps you could take the same amount of time to write a well-researched guest post, or some other type of op-ed piece.

That type of content is much more likely to earn the type of high quality targeted links you're looking for, without junking up your link profile.

In that case, I would probably focus my efforts on a parent page. The keywords you are probably targeting won't have a lot of competition, and a high ranking top level landing page will also contribute to the rankings of lower level pages.

In addition, the concept of "Evergreen" comes to mind. When you cycle through model numbers or inventory, you would lose the value you've built into the lower level pages. If, instead, you focus on your top level "Evergreen" pages, you can update those pages without losing rankings.

Tagging posts provides a good user experience, allowing them to scan through a number of related posts. It does create a number of duplicate content issues though.

To solve this on my own wordpress websites, I've added a noindex tag to each of the "archive pages", which includes tags, categories, authors, and dates. This effectively cuts out the duplicate content areas and I haven't seen any unusual fluctuations in search traffic.

PDF's are crawl-able, see this article from Webmaster Central

With that in mind, it's also a good idea to have the content available online as HTML. It's accessible from a wider variety of devices, and doesn't require you to update your adobe reader.