I need to know if any mugshots website like Mugshots.com is permitted to post mugshots of minors.

Sure... why not? As long as its legit, and not pornographic in nature.

Are the minors being tried as a adult or as a Juv.

Example, here in GA, they are charging a 16 as a adult on a rape case that happened yesterday.

In some jurisdictions, law enforcement agencies are not permitted to release information about minors who are alleged to have committed offenses. However if that information is released, Mugshots.com or other examples of "the press" have a constitutional right to publish it.