You situation is one that happens frequently. Here are some answers:
1. You have no right to any severance, unless you have a contract, or there is some employee benefit plan, that specifies severance. If there's no such contract or plan, you get what you can negotiate, and the company will always want a quid pro quo -- as you're seeing.
2. Non-compete's are hard to evaluate. They need to be reasonably limited by time, geography and subject matter. But there is a lot of variability in how a court may interpret "reasonable". Also, a court can "blue-pencil" the non-compete, meaning it can modify it to make it enforceable, instead of throwing the whole thing out. Finally, the costs of litigating the enforceability of a non-compete can be daunting. So I always advise my clients to assume that the non-compete being negotiated will be enforceable. (Obviously, it's a different analysis after the fact, when a client comes in with an already-executed non-compete).
3. YOu need to evaluate the cost of the potential future business you are being asked to give up, compared to the value of the severance package the company is offering you