1) HALACHAH: EATING BEFORE THE ONE WHO SAID "HA'MOTZI" EATS
OPINIONS: The Gemara says that those who are sitting at a meal may not eat before the person who recites "ha'Motzi" eats. There are two opinions as to what this means.
(a) TOSFOS (DH Ein ha'Mesubin) explains as follows. First, those who are sitting are not allowed to eat first if they are going to be eating from the bread that is before the leader. Second, those who are sitting are allowed to eat first if they have their own loaves in front of them from which they will eat after the leader recites the blessing for them.
The logic for the first ruling is as follows. One must recite a blessing over a piece of bread which is before him. If those who listened take a piece of the leader's loaf before he does, they have fulfilled their obligation to say a blessing, but they have not fulfilled their obligation to say a blessing on a loaf that is before them -- since it was before the leader at the time of the blessing. If the leader eats first, then the others fulfill their obligation not only to say a blessing, but to say a blessing on a loaf that is before them (since the loaf was before the leader when he said the blessing, and he represents them in this blessing).
(b) Tosfos cites the SAR M'KUTZI who gives a different explanation. If the person who recited "ha'Motzi" distributes pieces of bread from his loaf to everyone at the meal, they may eat before he eats. The Gemara is saying that before the leader distributes the bread to them, they may not reach for the bread in front of the leader and take a piece before he takes for himself.
According to the Sar m'Kutzi, it appears that this Halachah is not part of the laws of blessings. Rather, it is part of the laws of respectful manners (Derech Eretz).
HALACHAH: The SHULCHAN ARUCH (OC 167:15) cites the first explanation of Tosfos, that people should not eat before the one who says the blessing, unless they have their own breads in front of them. The MISHNAH BERURAH (167:83) points out that Shabbos is an exception. Even if they all have their own loaves of bread before them, they may not eat before the leader, because they are required to eat from his Lechem Mishneh (his double portion of bread). If they all have their own loaves of Lechem Mishneh, though, they do not have to wait for the leader to eat.
In addition, when the leader makes a blessing on a complete loaf of bread, and those listening only have slices of bread in front of them, they must wait to eat until the leader has eaten, because it is preferable to make a blessing on a full loaf rather than on slices.
2) HALACHAH: INCLUDING AN "AM HA'ARETZ" IN A "ZIMUN"
The Gemara states that an Am ha'Aretz may not be part of a Zimun. TOSFOS (DH Amar Rav Huna) says that nowadays we do invite an Am ha'Aretz to join. Today, the ignorant people are not able to accept that they are inferior to Talmidei Chachamim, and they will completely separate themselves from the community if we do not involve them in our religious affairs.
HALACHAH: The SHULCHAN ARUCH (OC 199:3) rules like Tosfos. The MISHNAH BERURAH (199:2) adds that a Jew who has strayed so far from the Torah that he purposely and maliciously transgresses the Mitzvos in public may not be included in a Zimun.