-- 公司给$2x1000股, 简单点就说一次而不是四次.
This is called grant. No tax, since you are granted the right, but you don't have any options at this moment.
-- [you missed the step of vesting here. For example, your options are granted equally in 4 years, that is, 250 shares per year. After you work there for one year, you have 250 shares vested. That means, you own 250 shares of options. To simplify the answer, since you are working in a start-up, that is, it is non-public, you don't need to pay tax]
-- [At the end of year 2, you have another 250 shares vested. Suppose you want to buy them, that is, exercise them. If the valuation of each share is $2.50 at this moment, then first, you pay 500 shares * $2.50 = $1250 to buy the shares. Second, you need to pay tax on your earn on paper, that is, 500 shares * (2.50 - 2) = $250. Note that your start-up is still private, and we suppose there is no second market for your shares to sell, you still need to pay the tax, even though $250 earnings is on paper only.]
-- Suppose your start-up goes public, and you sell the above mentioned 500 shares at $50 per share, then you pay tax on 500 shares * (50 - 2.50). Note it is minus 2.50, not 2.00.
-- Suppose your start-up doesn't make it. Most probably the options you have will be worth nothing. If you exercise your options, you not only lose the money spent to buy them, that is, $1250, as in the example above, you also lose the money that you pay the tax.
-- On the other hand, if you are sure your start-up will make it, then exercising at an early time may benefit in terms that 1) you may have a lower tax rate at that time, -- your total income could be much higher when you get rich from your start-up going public. 2) after exercise, they are stocks, not options. Then there is long-term capital gain tax benefit. For example, if you exercise right after your star-up goes public and lock period expires, (6 month is the common duration), the tax rate is supposed to be short-term, which is your income tax rate. If you had exercised one year before going public, then you only long-term capital gain tax rate, which would be much lower than your income tax rate, considering you most probably would have very high income then
Edit: typo