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How does this affect my styles/CSS?

Not at all. The external class name is not used for any styling purposes, and you can just combine it with whatever class names you're already using, eg: class="external my-other-class"

Does this work on admin pages?

No, it only modifies links on non-admin pages (this is by design).

Can I change the required class name from `external`?

Yes, simply open external-linker.php and change the EXTERNAL_LINKER_CLASS_NAME constant.

Can I turn off the automatic post filter?

Yes, simply open external-linker.php and change the EXTERNAL_LINKER_USE_FILTER constant to false.