What determines who has authority to sign a contract on behalf of the company?
What if a low level employee signs a contract in the name of the company, is it still binding?
What happens when there are conflicting contracts signed by different people in the company?
This is a rather complicated subject.
To start, you need to distinguish between authority (what the company says an individual is allowed to do on its behalf) and power (under certain circumstances, an unauthorized individual may be able to bind the company to a contract, anyway).
Furthermore, analysis of a given situation will depend on applicable state law (assuming you are in the US) and whether the company is a corporation or LLC (or something else).
Disclaimer: This information does not constitute legal advice and does not establish an attorney-client relationship.
The answers to these questions depend on the details of your particular situation. I'll give you some general ideas, but if you are having these kinds of issues you really need to retain an attorney who will get all the facts and give you a more precise answer.
The general area of law is called agency.
(1) The company determines who has authority to sign a contract on behalf of the company. For a startup, this is often not done explicitly, but if someone is signing contracts on behalf of the company, and the CEO knows about it, then there is an implicit acceptance of this. Bigger companies will be more formal about it.
(2) If a low-level employee signs a contract on behalf of the company, it is likely not binding on the company. The general principle is one of reasonableness. It is not reasonable for the other party to believe the low-level employee has authority.
(3) If both contracts are valid and truly conflicting, then the company will probably have to breach one of them,