The myDebug-xxxx.log files are recording all PHP errors (syntax errors, fatal errors, etc) which are occurring while people are clicking around in your site. You should fix whatever errors are being reported, as some of them might actually be causing pages not to work for some customers, and thus maybe you might be losing customers.
The AIM-debug log files are tracking transaction attempts where your customers choose Authorize.net as their payment choice. If your payments are coming through fine, these will likely all show Success. That's good. If they're showing failures, then your customers were told they can't checkout with that card, and were asked to choose another payment choice.
Summary:
The .htaccess and index.php files are there for security reasons. They should not be touched.
The sess*.* files are customer shopping sessions and should not be touched unless older than yesterday.
The zcXXXXXXXX.sql files are SQL cache objects, and should not be touched unless older than yesterday.
The *.log files are log files, and can be deleted if you've dealt with whatever problems are recorded therein, if any.
As far as the *.log files go, Yes.
In v1.3.9 there is an option in Admin->Tools->Store Manager to delete old log files. You might want to take a copy of them first if you've not yet dealt with certain errors they're reporting to you.
Searching for "database backup" in the FAQs/Tutorials area of this website brings up this as the first article: https://www.zen-cart.com/tutorials/i...hp?article=103




