A. A direct democracy is a democracy in which there are no such things like presidents or similar things and all people participate in voting, literally all. Whenever there's a decision to be made, all people go out and vote and the choice that gets the most votes is what happens with the country.
B. In a republican form of government, democracy is practiced by people voting on whom they would give the power to represent them, such as a president or a similar figure. The sovereignty lies with the people who vote on a person who would make the choices regarding the state for them so they don't have to vote all the time like in a direct democracy.
C. A direct democracy can easily lead to the tyranny of the majority since the majority would easily choose what suits it and minorities would have a lot of issues with their rights. In addition, in a huge country, a direct democracy is not good because people from various parts of the land don't understand the problems of those from other parts of the land and don't care much about them.
D. i. In a trustee model, the decisions that the representative of the people makes are based around their own sets of values under which they were chosen and people believe them that they will make the best possible decisions when it comes to deciding what choices are the best for the public good.
D. ii. In a delegate model, the representational model, the representative of the people makes the choices regarding the state not on what they believe or think should be done but rather are instructed by the people on what should be done and how. There is a lot less personal integrity as they just represent the group with their choices, they don't make their own choices.
E. This depends on numerous factors. It depends on what questions and choices are at stake, or it depends on the access of information of either the representative or the people. It also depends on how well a representative can determine what the voters actually want. Sometimes they make decisions that people don't want but they eventually turn out to be good and people start understanding that they were good decisions.