I looked at your site in Firefox 56.0.2, didn't notice any obvious problems.
I can't solve your new problem, but i can give you some suggestions for working in that direction.
1 - Housecleaning. Your entire site is located within one folder on the live server. FTP that folder down to a backup folder on your PC. It may take a long time, like hours, because the folder will contain numerous small files, which slows the data rate. Keep this backup folder intact and safe and unedited.
Then figure out which "copy or version" of your site on the live server is actually the one driving your website. Delete the other copies or versions from the live server. You need to get to a point where the only files and folders on the live server are the ones that are running your site. Get your host to help you. If I understand you correctly, there may presently be multiple versions. That won't help with SSL issues.
If you break something, restore things from the backup folder on your PC until the site runs. Keep notes as you clean up.
2 - Read the AC documentation on Developer Tools and cloning the default template. I doubt that your host-created website clone is the same concept as an AC template clone used for customizations. If you use AC Developer Tools to create an AC Template clone, you will see the clone in it's own folder within the root/extensions folder, and that folder will have a name that you chose (templatename), and it will contain a cluster of site folders within a /storefront/view/templatename/ hierarchy. If you can't find this in your site files, then you don't have a template clone. This is not relevant to your SSL problem, rather just an FYI. If you study enough to understand my comment, you will begin to understand how AC works.
3 - Structure. You need to learn how the site runs from the server. AC is an application. There are a small handful of files on your server that tell the AC application how to start up and run. After that, it just runs. Study your htaccess file, see what is in it. In particular, you need to understand the RewriteEngine family of commands that include RewriteCond, RewriteBase, RewriteRule, etc. There will be several of these rules in htaccess, and the settings specified by these rules basically contribute to either smooth sailing or endless headaches.
4 - Here is a cut-n-paste from my notes for initial live site setup:
c. Rename the htaccess.txt file to .htaccess.i.
ii. The dot in front of “.htaccess” indicates that this file is ‘invisible’. Therefore you may have to configure your FTP application or hosting file manager to show invisible files in order to edit. This .htaccess file on an Apache based web server allows you to configure settings for how you’d like your website, or certain files within your website, to behave.
d. Edit the .htaccess file: if your store is not on the root, you have to configure the RewriteBase/ element to point at the subfolder that contains your store: change it to RewriteBase/subfoldername/ . The ending slash is important.
e. AC Admin control panel - System>Settings>System:
i. Scroll to bottom, enable System Check for Admin and Storefront. Then check the messages that will come up on Admin as you use it. Resolve the messages. Delete each after you resolve it.
ii. Turn on Retina.
iii. Turn on SEO URL's
iv. Note: these all require the mod-rewrite Apache module to be active and .htaccess.txt to be renamed to .htaccess and the RewriteBase/ to be properly configured.
If you read up on the terminology in the snippet 4 above, you should begin to understand what htaccess is doing, which is a step towards getting it set properly.
My htaccess file includes the following rules that steer all traffic to https :
RewriteCond %{SERVER_PORT} 80
RewriteCond %{REQUEST_URI} !^/[0-9]+\..+\.cpaneldcv$
RewriteCond %{REQUEST_URI} !^/\.well-known/acme-challenge/[0-9a-zA-Z_-]+$
RewriteCond %{REQUEST_URI} !^/\.well-known/pki-validation/[A-F0-9]{32}\.txt(?:\ Comodo\ DCV)?$
RewriteRule ^(.*)$
https://www.yoursitenamegoeshere.com/$1 [R=301,L]
If you aren't set up properly in this fashion, that will be the first place that SSL problems start.
If you get htaccess "right", then your host is going to be the one to help you resolve remianing ssl probs.
Good luck. I was almost as much a noob as you when i started. It took me months to sort this stuff out. There are no shortcuts or quick fixes, other than cash. If you want a super quick and dead-right fix, contact the AC devs and ask to them to do a contract job to clean this up. I would imagine they could fix everything for less than the cost of a weekend's entertainment.