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.