Speaking purely from a logical perspective, if you are working at the pound, there is an automatic assumption of risk that any employee obtains that an animal may bite, scratch, or otherwise attempt to attack the workers. The warning the employer provided is quite valid and that by itself is not a violation. While it is not 'acceptable', it is a real danger. It may create liability if the injury is serious enough where you may need to seek workers compensation benefits but it is somewhat difficult to not expect biting if you work at a kennel--that is indeed part of the job. The same potential risk may be working at day-care--children can bite those who work with them, although I am not equating children with animals, merely with a similar sort of risk.
In terms of watching you on film, New Jersey laws permit employers placing cameras on site, just not in truly private areas such as bathrooms or locker rooms. Being told that you are being filmed is simply putting you on notice, but it does not violate state law if you are being filmed. If he does film you elsewhere, it can create violations and potentially permit you to file for a cause of action and damages.
Having worker's compensation is an insurance coverage policy
that makes employer liable for personal injuries
that employees sustain while being on employer premises or working for them. In this situation if you seriously hurt your wrist and it is in pan, you can potentially request the employer's insurance information so that you can file a claim and have the coverage cover your medical costs if any. That is why it is important, it can help you cover costs from hurting yourself while working for this employer. This is obviously very important if you are already injured and may be injured further.
Ultimately it sounds as if this job is completely not what you expected. In that situation you really have two options--you can either tough it out because the situation likely will not change for the better, or you can quit and find something better. So far the employer has not demanded or requested that you do anything outside of your scope of employment as a 'manager' in a kennel (since a manager is supposed to know all aspects of employment), but if you feel it will get worse, consider finding something that is more aligned with your expectations.