It seems like there are people reading this thread who are much more knowledgeable than I am, but I saw these questions and thought "Ooh, ooh, I can take those!" So, here's my best shot:
1) I don't think anyone believes that you can't convert to Judaism. Ruth, the ancestress of King David (and through him, the Messiah), was a convert. In fact, most of our philosophy about conversion comes from the book of Ruth. What these Orthodox Jews do believe, as far as I know, is that, the modern world being what it is, they don't trust the validity of any conversions currently being performed.
I know several people who were converted by my Local Orthodox Rabbi, and the process they underwent was about a year of extensive study of the laws that they would have to take on as Jews, followed by an oral examination by the Beis Din, the religious court. Once they passed, they take a dunk in a ritual bath and get a certificate basically saying "The Rabbinate of Pittsburgh certifies that so-and-so has undergone a valid conversion."
But here's where it gets sticky. My LOR is Modern Orthodox, and so people who study under him learn his (Moden Orthodox) philosophy and rulings. Which is good enough for the vast majority of Jewish communities in the world. But there are a few ultra-Orthodox communities who would disagree with the stringencies or leniencies that he teaches. So a convert who studied with him didn't really learn and take on the law, as they see it. Therefore the conversion isn't valid.
2) This is one of those things that comes from Ruth. If you look, when Ruth told Naomi that she wanted to return to Israel with her ("whither thou goest, I will go; and where thou lodgest, I will lodge; thy people shall be my people, and thy G-d my G-d"), Naomi tries three times to dissuade her.
The main idea is just what kahnman said. Following the Noahide laws is an equally valid path. Once someone becomes a Jew, they can't choose to "un-obligate" themselves from all of the commandments. Why take on so many extra laws when it doesn't gain you anything?
3) Because G-d didn't command it of you. And who are you to decide that G-d chose the wrong path for you?
Re: Paths
1) I don't think anyone believes that you can't convert to Judaism. Ruth, the ancestress of King David (and through him, the Messiah), was a convert. In fact, most of our philosophy about conversion comes from the book of Ruth. What these Orthodox Jews do believe, as far as I know, is that, the modern world being what it is, they don't trust the validity of any conversions currently being performed.
I know several people who were converted by my Local Orthodox Rabbi, and the process they underwent was about a year of extensive study of the laws that they would have to take on as Jews, followed by an oral examination by the Beis Din, the religious court. Once they passed, they take a dunk in a ritual bath and get a certificate basically saying "The Rabbinate of Pittsburgh certifies that so-and-so has undergone a valid conversion."
But here's where it gets sticky. My LOR is Modern Orthodox, and so people who study under him learn his (Moden Orthodox) philosophy and rulings. Which is good enough for the vast majority of Jewish communities in the world. But there are a few ultra-Orthodox communities who would disagree with the stringencies or leniencies that he teaches. So a convert who studied with him didn't really learn and take on the law, as they see it. Therefore the conversion isn't valid.
2) This is one of those things that comes from Ruth. If you look, when Ruth told Naomi that she wanted to return to Israel with her ("whither thou goest, I will go; and where thou lodgest, I will lodge; thy people shall be my people, and thy G-d my G-d"), Naomi tries three times to dissuade her.
The main idea is just what
3) Because G-d didn't command it of you. And who are you to decide that G-d chose the wrong path for you?