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The answer depends on your employer's policies and your employer's reason for searching. If something of great value to the company has been stolen that day, and the employer decides to search people in a reasonable way (for example, searching their bags, not their bodies), then it may be legal -- particularly if your employer has a written policy warning employees that they might be subject to search. However, an employer who does this as a daily routine will be on shakier legal ground.
The answer depends on where the employer wants to put the cameras and why. The employer must have a reasonable, legitimate business reason for monitoring employees in this manner (for example, to discourage theft from a cash register or to enhance the security of customers and employees). And some states have made certain areas of the workplace (for example, the bathroom and changing areas) off-limits to this type of monitoring.
Even with a legitimate reason, your employer must inform you and your coworkers that the cameras are there. Also, some states prohibit the use of certain types of surveillance devices, such as one-way mirrors.
Your employer cannot fire you for your religious or political beliefs. Federal and state laws (and the First Amendment to the U.S. Constitution, if you are a public employee) protect workers from this type of discrimination. However, if you bring your beliefs into the workplace in a disruptive way -- for example, by attempting to convert coworkers to your religion or by campaigning for a political candidate on work time -- then your employer may legally put a stop to your conduct. For more information on religious beliefs, see Your Rights Against Religious Discrimination.
Psychological tests given by employers are highly questionable and often invasive. If the employer doesn't seem to have a sound reason for giving the test, and if the questions make you uncomfortable, then you might have a legitimate claim that the employer is violating your privacy rights.
Generally, yes, depending on your employer's policies. If your employer has a policy saying that the computer and email systems should be used for business purposes only, then it has the right to monitor your email. If, however, it has policies that lead you to believe your email is private, then its rights may be more limited. As a practical matter, however, most courts to consider email privacy claims have found in favor of the employer, regardless of its policies.