So, to ka9q's specific questions:
I know the main difference is we have a presidential system in which a separately elected chief executive runs a separate executive branch of government while you have a Parliamentary system in which the executive is the leader of the majority party in the legislature. While our elections occur on fixed timetables and it is intentionally difficult but not impossible for our Congress to get rid of the US president before an election, you have something called a "vote of no confidence" and seem able to call elections and change prime ministers on short notice.
Okay, a few issues here. It's also worth noting that processes differ across jurisdictions.
Fixed term elections: This occurs in some Parliamentary systems. For example, here in Australia, several states have legislated for fixed terms. This simply means that, if nothing else goes wrong, the next election will be in three years (or whatever the chosen duration is).
However, at the Federal level in Australia, three years is simply the maximum term for a Parliament, and the PM can always ask the Governor General to dissolve Parliament early. This can be a risky decision: it might be tempting for the PM to call an early election if the Opposition is in disarray, but if the decision is seen as being purely for such political reasons that might not go down well with the voters.
But even with fixed Parliamentary terms, it might occasionally happen that an election would be called early. If that happened, then the next election after that would simply be three years after that early election, thus setting up a new electoral cycle.
Vote of No Confidence: As mentioned earlier, the government is formed by whichever party holds the majority in the House of Representatives. Most of the time this isn't an issue - at the 2013 Federal election, the Liberal-National Coalition won 90 seats out of 150, so it easily formed government. Party discipline is very strict in Australia, so it's very unlikely that sitting members would vote against their party.
However, the previous election in 2010 saw the Australian Labor Party (ALP) forming a minority government with the assistance of independent Members of the House. As it happened, that Parliament lasted its full term. But if one or more of the independents had become seriously disillusioned with the ALP some time during the Parliament, they might have moved a Motion of No Confidence. If that vote were to be passed, the government would fall, and the GG would have asked the Leader of the Opposition to see if he could form a government. If not, we'd probably have ended up going to an early election.
The last time this happened in Australia was in 1941, when two independents held the balance of power in the House. Disillusioned with the performance of the then conservative government, the independents switched their support to the ALP, which then took over government. In a rare act of activism, the then GG leaned on the two independents, asking them to keep supporting the ALP government until the Parliamentary term was finished, to avoid the need for an early election in the middle of a war.
Changing Prime Ministers: This can happen two ways. The usual way (
ahem!) is if the PM's party loses an election. In that case the now former PM becomes the Leader of the Opposition (or resigns the leadership, resigns from Parliament, writes memoirs which sell badly, and earns a heap of money on the high-level speaking circuit).
The second way the Prime Ministership can change is if the governing party decides to change leaders. Until only a few years ago, this could happen with either major party simply by a majority vote of Parliamentary members of that party. The first time that happened in Australia was in 1992 when ALP PM Bob Hawke was dumped by his party and replaced by his former Treasurer, Paul Keating. (Liberal Party PM John Gorton was replaced by
his Treasurer Billy McMahon in 1971, but in that case the party room vote was tied and Gorton decided instead to resign rather than continue to lead a party which was obviously so divided.)
This method has since been used by the ALP twice and the Liberal Party once, all in the last six years, which is why the PM's office in Parliament House now seems to have a revolving door fitted to it. In 2010 ALP PM Kevin Rudd was dumped in favour of Julia Gillard. Then, in 2013 Gillard was in turn dumped to allow for the return of Kevin Rudd. Then, after winning the 2013 election, the Liberal Party in 2015 dumped PM Tony Abbott in favour of Malcolm Turnbull. It's perhaps not surprising that some people have looked back nostalgically to the Prime Ministership of John Howard, who led Australia unchallenged from 1996 to 2007. However, after Kevin Rudd regained power in 2013, he arranged for the ALP to change its rules so that the party leadership had to be voted on by ordinary party members as well as the Members and Senators, so at least for the ALP party leadership has become a more stable position.
I know that although we both have two houses in the legislature, our "higher" house is elected and yours isn't. Our system seems structured to perpetuate two dominant political parties because of a "prisoner's dilemma" type situation discouraging votes for third parties; in your system, multiple parties and coalitions seem common.
Upper House: Yes, members of the House of Lords (and also the Canadian Senate) are appointed. However, as mentioned earlier, in Australia we elect our Senators - 12 for each state and 2 for each territory, for a total of 76. Senators are elected using a form of proportional representation which is tricky to explain and takes even longer to resolve. We've been told it may take a month to work out who's won Senate seats out of this election.
Incidentally, the electoral process for Senators in Australia is that they normally serve two Parliamentary terms, so in a normal election only half of them are up for election (well, half the Senators representing states - territory Senators face voters every election). However, if the Senate votes down a House bill three times, the PM can apply to the GG for a Double Dissolution election, in which all Senators are up for election. That's what happened at our election last weekend. Then, when the new Senate meets for the first time, they have to work out which of them get the six year terms and which the three year terms. As there aren't any laws governing this, and as the government is going to have to work with a hostile Senate, it'll be interesting to see what they come up with.
Two dominant parties: While the USA is dominated by two political parties, so is the UK, and, for that matter, so is Australia. In the case of the UK the dominant parties are the Conservative Party and the Labour Party. The Liberal-Democrats were important only after the 2010 election because they happened to hold the balance of power in the House of Commons, and thus were able to choose which out of the Conservatives and Labour to back. Most of the time one party has a comfortable majority in the House.
It's the same in Australia, where from 1943 to 2010 either the ALP or its conservative opponents held a majority in the House of Reps (although from 1961 to 1963 that majority was 1).
The reason both the American and Parliamentary systems have tended towards two-party systems is simply a consequence of having single-member electorates. By contrast, in legislatures where politicians are elected by some form of proportional representation then a wider array of parties are represented. This is shown in Australia by the Senate, in which in the last 36 years the government of the day has held a Senate majority for only a single three year term. Likewise, here in the Australian Capital Territory, where our Assembly is elected by a form of proportional representation, we've had one term of majority government in a total of eight Assemblies.
In our system, impeachment is just one element of what seems to be a much more explicit separation of powers and "checks and balances" between branches of government. And of course we have all this in a written constitution that everyone at least claims to hold in very high regard, and which is formally interpreted by a separate branch of government, the judiciary, using a system of common law that we inherited from you guys.
True. Separation of the powers is provided for in the Westminster system, but I think it's less explicit than in the American Constitution, particularly given that the Executive is effectively part of the Legislature. But I'm not confident about this aspect of our form of government, so I'm not going to comment too much about it.
However, I can say with certainty that the Judiciary is independent of the Legislature and Executive, and one of the jobs of the High Court of Australia (~ the US Supreme Court) is interpretation of the Constitution. Still, having said that, yes, High Court judges are appointed by the GG on the advice of the PM, and they aren't subject to acceptance hearings. Despite that, appointment of High Court judges seems to attract a lot less heat and light than it does in the USA.
Yet one weakness of the Australian Constitution is that the checks and balances are a little more wobbly than in the American Constitution. For example, the Queen appoints the GG on the advice of the PM, while the GG appoints the leader of the largest party to be PM. Thus, effectively, the PM and GG appoint each other; they also have the power to dismiss each other. This nearly became an issue in 1975 when the then GG Sir John Kerr sacked the PM Gough Whitlam over Whitlam's inability to get a hostile Senate to pass his Budget. Without going into details, Kerr gave Whitlam no indication of his thinking, called him to his office and told him he'd been dismissed. The reason Kerr gave Whitlam no warning was his fear that Whitlam would then call the Queen and advise her to dismiss Kerr, advice the Queen was required by convention to follow.
