1) A lot of people in America drink חלב סתם, are they relying on רב משה , if yes, he only said it if you can’t find חלב ישראל , Do you know who they’re relying on? 2) what did Rabbi Soloveitchik hold?

Shalom, Thank you for your question. You are correct that many people who keep strictly kosher in the United States drink government supervised milk (chalav stam) rather than milk supervised by a Jew (chalav Yisrael). Although the Rabinic obligation to drink only chalav Yisrael is the halacha as ruled in the Shulchan Aruch – those who are lenient and rely on good non Jewish supervision certainly have halachic sources to support them. The major kashrut supervision organization in the USA is the O-U, who allow chalav stam, and label it with an O-U D[airy] hechsher. As to the halachic source for this leniency, again you are correct that Rav Moshe Feinstein zt”l was a major source for saying that government supervision is halachically equal to Jewish supervision. None the less, he did allow for the fact that a ba'al neshef (a person who is supercilious in there service of Hashem) should be strict. In another of his responsa (Yoreh Deah 4,5) he writes that it is permitted to be lenient in “sha'at ha'dochak” - a trying situation. There are various understandings of when and for whom Rav Feinstein zt”l would have (and did) rule leniently or strictly on this question – some Rabbis understand him more strictly and others more leniently. However, Rav Feinstein zt”l was not the only Rabbi to use this argument. It can be found in the writings of the Chazon Ish (Y.D. 41,4), as well as in other sources. There are those who use the argument of Rav Feinstein zt”l (and the Chazon Ish) without holding his view that this is a limited leniency – rather they hold that one may rely on this logic in all situation. As well as this argument, there is an early argument written by the Pri Chadash (see Darchei Teshuva 115:6 who quotes others who hold like this opinion) that holds that where non kosher milk is not available, or is more expensive, one does not need Jewish supervision on the kosher milk, as we can assume that there is no incentive for someone to lie and sell non kosher milk for a loss. And although many Rabbis argue with this opinion – perhaps when put together with the opinion about governmental supervision, it may be an opinion that can be relied upon by all. In short – those who are lenient do so for a number of good reasons. Firstly, their situation may be one of need (and one should never rush to judge what is considered need for another Jew, as everyone's physical, and more so, their spiritual situation is different. ie. People grow at different paces). Next, perhaps Rav Feinstein's argument can be relied upon even not in situations of need (even if he himself ruled more strictly, other Rabbis may rule more leniently). Also, there are other grounds to be lenient. Here is a good article that outlines these and other issues - https://www.theyeshivaworld.com/news/headlines-breaking-stories/269442/halachically-speaking-cholov-stam-and-cholov-yisroel.html As to Rav Solovi view – I quote from an article by Rav C Jachter on YU Torah (Chalav Yisrael - Part I: Rav Soloveitchik's View) “It is well known among Rav Soloveitchik's students that the Rav when he resided in the United States drank packaged milk that did not have any special Rabbinic supervision. Rav Genack mentioned in a Shiur at Yeshiva University that the Rav told him that there exist three considerations to be lenient. First, if no non-Kosher animals are found in the herd of animals that is being milked (“Ein Bedro Tamei”) some authorities rule leniently. Second, we may rely on the government (USDA) supervision and inspections to insure that the milk we consume is from cows. Finally, the rabbinic edict forbidden drinking milk from an animal that was milked by a non-Jew technically does not apply today since the cows are milked by machines.” https://www.yutorah.org/lectures/lecture.cfm/735843/rabbi-chaim-jachter/chalav-yisrael-part-i-rav-soloveitchik-s-view/ Blessings.