Some CMS would do that automatically, if the company you are working with had one of those (or the decision maker is used to seeing that) they may just think that it is normal and a best practice. At the end of the day, while odd now, it should not matter from an SEO perspective (just make sure that you redirect the base url to that page).

All you will need to do to fix any problems from a search perspective is create a canonical tag that points at your preferred home page and place it into the meta on your home page so it will be shown across all variations by the CMS.

While you might see a small down tick in the beginning as Google indexes and updates, overall you should not suffer any long term negative effects from standardizing your URI structure.

Also, your Google traffic and your Adwords will never line up perfectly due to the difference of how each is tracked.

Google has gone into the differences here:  https://support.google.com/analytics/answer/1034383?hl=en

Did you link your GA and Adwords accounts or are you just tagging?  Organic (not provided) is how GA shows all search traffic from users who connect to Google securely (signed into a Google account) so this could be branded traffic but there is no way of knowing in GA.

In general structure changes can cause changes in traffic, for your conversion you should also look at your GA goals and how (if any) your events are programmed.

If you switched from http: to https: you need to change your GWMT. Your GA account is linked to your old GWMT for non-secure, you will need to set up a new GWMT account for secure (https:) and then link that with your GA account.

While I would need a lot more information or time in your GA to get to the bottom of this, here are some questions:

Did you make any changes to your site code or GA account settings in February?

Did your impressions fall during this time as well or just your clicks?

Are your keywords seasonal, based on specific dates or events?

Do you have an alert in GWMT about your site?

It is best practice to use nofollow tags and your robots.txt to keep search engines out of not only e-commerce pages, but also any areas that require a log in (such as a customer profile page or shopping history).  You want to do this so that they do not accidentally index pages that will redirect users who aren't logged in or create a weird/negative experience for them.

If you can actually load the regular URL then you should canonical to it (it is best practice to canonical all of your pages to themselves), but if going to that page just redirects to the escaped fragment then you should update how your site build is set up so that you don't have the escaped fragment any more.

Write as much copy as you need to convey the information that is needed for your visitor on that page.  If you can create a good user experience on one page with 100 words (by answering the pain that they would be going to that page to solve) and then you need 1,000 words for your next page, then do that to.  Don't make arbitrary copy limits or goals based on SEO, make your pages user friendly and your copy useful and your pages will rank well for the appropriate content.

Also, your Google traffic and your Adwords will never line up perfectly due to the difference of how each is tracked.

Google has gone into the differences here:  https://support.google.com/analytics/answer/1034383?hl=en

It is best practice to use nofollow tags and your robots.txt to keep search engines out of not only e-commerce pages, but also any areas that require a log in (such as a customer profile page or shopping history).  You want to do this so that they do not accidentally index pages that will redirect users who aren't logged in or create a weird/negative experience for them.

Meta descriptions do not effect your page optimization in the sense that a search engine is effected by it, but it will effect how often people click to your site as the meta description is the copy a person is shown. You should make your descriptions informative and truthful so that it accurately portrays what each page has to offer giving a potential visitor the best ability to judge what content will be on the page (and thereby lowering bounces/re-searches). This being said you should write custom meta descriptions, not just let it truncate content already on your page.  I would start with products that are relevant to the most used keywords and work backwards, if you dedicate yourself to doing at least 20 descriptions a week you will have all of your legacy products done in a year.

The easiest way to do this is to export the data and work with it outside of Google Analytics. I reccomend using http://www.nextanalytics.com/ to automatically export data from GA into excel.

If you switched from http: to https: you need to change your GWMT. Your GA account is linked to your old GWMT for non-secure, you will need to set up a new GWMT account for secure (https:) and then link that with your GA account.

Have you tried searching the account number to see what other websites (if any) are using that account? If you client's UA number does not end in a -1 then there is a good chance whomever made the site used the same account for all of the work they did, including their own site.

While I would need a lot more information or time in your GA to get to the bottom of this, here are some questions:

Did you make any changes to your site code or GA account settings in February?

Did your impressions fall during this time as well or just your clicks?

Are your keywords seasonal, based on specific dates or events?

Do you have an alert in GWMT about your site?

In general structure changes can cause changes in traffic, for your conversion you should also look at your GA goals and how (if any) your events are programmed.

What do you mean "pages that have nothing to do with my site" are these not on your domain or are they on your domain but you are not familiar with them?