We can ask anything. No law prevents us doing so. A few laws prohibit answering some questions. Some laws prohibit our considering some applicant info in making hiring decisions.
Present employer is allowed to call past employer. However, past employer is not obligated to say anything without a signed waiver from employee ... which is what most employers are doing now to...
You should not, the filtering is there for a reason and if you attempt to bypass it you will most likely be violating policy which could lead to negative action being taken against you.
They typically validate degrees. it is a simple data check. If you lie about them, you can find yourself fired with no recourse. And if it is a government job, you may find yourself facing criminal...