Can't locate where Commerce Authnet stores the API and Key
I'm assuming you're using the latest version of Commerce authnet.

Drupal Commerce payment system (as well as discounts, taxes..) is based in rules, you can see here how the settings form are included: http://cgit.drupalcode.org/commerce/tree/modules/payment/commerce_payment.rules.inc#n250 in the rules UI, so it is basically stored by rules in a rules_config object, specifically in the unserialized data column.

So if you want to see the settings in the database, you can go to rules_config table and check the data db field.

Modifying this from outside rules is another story, I've never done this, but I'm quite sure that rules doesn't provide an API to alter this data field, you'll probably need to use the Database API to access rules_config table and unserialize/serialize the data information to alter it.

It is probably advisable to find an alternative way to do this, i.e providing a new module that runs a slightly modified version of the charge callback of authnet (http://cgit.drupalcode.org/commerce_authnet/tree/commerce_authnet.module#n750)