First question: Madison believed that the current state of the government, with the articles of confederation, enables factioning which could prove to be a great problem for liberty and for democracy. He believed that a strong constitution was necessary to protect people since uniting in a single republic and with a strong national government could help fight against factioning.
Second question: The anti-federalists might like it because he mentions that in a divided country there could be strife between states and states could have problems because of this. If a state became a supporter of the constitution and of federalism, they could all be equally protected by the national government.
Third question: This is a common thing in lawmaking and being a judge. There would be bias and a conflict of interest because you as a judge would be inclined to support an option which benefits you since nobody wants to rule against themselves. That's why judges cannot participate in any process that is in any way connected to them personally.
Fourth question: He claims that a democracy cannot be sustainable on a national level while republicanism can be applied to an entire nation regardless of its size. Basically, it means that the people from California for example wouldn't care much when it came to people in Florida in voting so they might fight only for their rights. If there is a republic, then both California and Florida would have equal rights according to the federal government and could participate and fight for everyone together.