Why “positive theory” is important in discussions of how antitrust law achieve “normative goal”?
Positive theory is important in any economic discussion. Positive economics is economics of what is, facts, data, theoretical relationship derived by logic from some axioms presumed to be true etc. Positive economics statements are statements like "unemployment rate in the US in October 2020 was 6.9%", or "in perfectly competitive market Price = Marginal Cost".
On the other hand normative questions are ought statements of what should happen based on some moral ideals or ideology. For example, "under Rawlsian principle of social justice poorest member of society should get welfare weight of 1 in social welfare function and all other people welfare weight of zero" is normative statement. That statement is not based on facts or empirics etc it is based on Rawls moral philosophy. Or for example, "government should try to maximize consumer's welfare by abolishing monopolies".
The reason why positive theory is important, is that the normative statement "government should try to maximize consumer's welfare by abolishing monopolies" requires us to first empirically, factually or logically (i.e. from perspective of positive economics) to validate the claim that dismantling monopolies will actually improve consumer welfare. Unless you involve positive economics how can you know it won't hurt the consumers?
1> Why does the author mention "perfectly competition market" in the first sentence? Whether the first sentence says that we need to based on what is really happening to plan for the strategy to achieve the goal?
Because author clearly argues that theory of perfect competition was important positive theory in area of antitrust, he would have not have written it if the author would not believe that.
2> Is the first sentence is explained as above, I do not understand what does the second sentence mean, it seems not link to the first sentence.
The sentence is linked, it says that positive theories are important in designing policy because they tell us which tools/policies/means we can use to pursue the (normative) ends we desire based on our moral values.
For example, whether state should force people to use medicine is normative question. But whether the medicine actually works is positive question. That sentence just says that it is important to get facts straight before starting to work on normative questions. Obviously, if the medicine is some bad snake oil and kills 90% of people taking, then that would change people's mind about the normative question of state mandating it. If on other hand the medicine has zero side effects and is life saving that again will affect people's decisions about whether normatively it would be good idea to force people to take the medicine.