Muggles' Guide to Harry Potter/Magic/Wizengamot

Overview
The Wizengamot is part of the ruling structure for the Wizarding world. It is first mentioned in passing on Albus Dumbledore's "Chocolate Frog" card, which tells us that he is Chief Warlock of the Wizengamot. Although it is never directly defined in the books, it is apparently a council of the most respected wizards, and is at least in part parallel to the Supreme Court in the Muggle world.

Extended Description
We see two incarnations of the Wizengamot directly.

In Harry Potter and the Goblet of Fire, Harry looks into Professor Dumbledore's Pensieve, where he observes the proceedings of the Wizengamot during several trials of Death Eaters shortly after Voldemort's passing. At that time, the head of the Wizengamot was Bartemius Crouch, and we see three different sessions: the session in which Karkaroff pleads to have his sentence reduced, Ludo Bagman's sentencing, and the trial (such as it was) and sentencing of Barty Crouch Jr., Bellatrix Lestrange, Rodolphus Lestrange, and Rabastan Lestrange.

In Harry Potter and the Order of the Phoenix, Harry actually has to stand before the Wizengamot in order to defend his use of magic against Dementors. Cornelius Fudge, the Minister for Magic, seems to be in charge of the Wizengamot at this point, having possibly replaced Dumbledore, and seems to be trying to use the Wizengamot as a means of doing damage control.

Analysis
Apart from the two versions of the Wizengamot described above, we can infer a third.

In the first version of the Wizengamot mentioned, during the Death Eater trials, the main function of the Wizengamot seemed to be trying and convicting Death Eaters. To that end, and reflecting the personality of the Chief Warlock, Bartemius Crouch Sr., it was a very harsh, almost militaristic organization.

When Harry is being tried, the Wizengamot seems to be in the process of turning into a mouthpiece for the Ministry. With Fudge as the Chief Warlock, its purpose has become very closely aligned with the needs of the Ministry, which like any political organization has a need for favorable publicity. To that end, the actions of the Wizengamot seem to be aimed at doing what will make the Ministry look good in the papers, rather than doing what will be the most fair; it is only the supreme debating skill of Albus Dumbledore that allows justice to be served in this particular case.

Finally, in between the two instances, there is mention that Albus Dumbledore is Chief Warlock of the Wizengamot, an office that he held until more or less forced out of that position by the Ministry over the summer before Harry's fifth year at school (Harry Potter and the Order of the Phoenix, chapter 5); and he does appear to be reinstated in Harry Potter and the Half-Blood Prince. His removal from the post does show that the Ministry has some indirect control over the makeup of the Wizengamot, although it seems that it is apparently supposed to be somewhat independent. One can assume, given Dumbledore's nature, that the Wizengamot under his control was concerned with truth rather than political expedience, and was a gentler and perhaps more noble court than in either of the instances we see directly.

Questions

 * 1) Dumbledore and Crouch are two people on the Wizengamot. Is there anyone else that we know who has been on it, or any position other than Chief Warlock?

Greater Picture
Unlike American and British Muggle democracies, there is only partial separation of powers between the Wizengamot and the rest of the Ministry of Magic. The Wizengamot appears to function as a High or Supreme Court, Criminal Court and Parliamentary and Legislative Body; a position not entirely unlike, and possibly inspired by, that which, at least in theory, the British House of Lords occupied at the time the first Harry Potter book was released.

During Harry's "hearing" in Harry Potter and the Order of the Phoenix the trial is presided over by Cornelius Fudge who acts as both prosecutor and principal judge (partly following on the Continental model, where the presiding judge himself takes part in inquiring about the crime). However, Fudge is also the head of government and administrative executive for the Ministry, and should not be permitted that much control and power. The author may have created such a flawed system to emphasize the potential for corruption and authoritarianism in the Ministry of Magic, or to emphasize the general old-fashioned nature of the Wizarding world (also seen on other occasions).