1. How is it decided that 10k stock options are worth $x?
2. Since it’s a start up the stock options are essentially of no value, correct? I don’t understand how these options have any value atm.
3. What does it mean when they say I can exercise the options upto y years after leaving the company?
2. Options that can't be exercised have no value. If your contract says you can exercise them, or a percentage of them, after a year, then that's the earliest point to have value. But there's no open market to sell shares. Your contract might even say you can only sell them back to the company. And when you decide to sell there needs to be an agreed price. By my experience (see below) the company might not want to name a price, add delays, point to near-future investment round, lowball you. They do have value, you do have the right to exercise but the actual exercise might lead to conflict with the founders because it's often not in their interest. The younger the company is, the earlier of an employee you are the more potential conflict.
3. That's actually good. Some contract say you have to exercise when you quit, or after e.g. 90 days. But you might think the company is growing well, stock will be worth more in the future and are allowed to hold on to the options longer. It gives you a bit more power.
Story time: two years after joining an early startup I decided I want to exercise some options, like 10%, almost just to see how it really works. The founders were very reluctant. They didn't worry about me leaving. They didn't care about the money itself. But the sale would force them to write down what a share is currently worth. They were negotiating with new investors, or planning in the near future. The investors would ask what the company is currently worth and this number would have to be presented again to the investors. They worried so much I got a cash bonus for NOT exercising options.