Everyone elects a member of parliament to the House of Commons. That's it. Our ballots have a single choice on them.

The Prime Minister is just whichever guy a majority in the House of Commons can agree should handle the day-to-day stuff. They have little in the way of codified power, but in practice operate fairly similarly to the US President--selecting ministers to lead key agencies, making orders in council ("executive orders") where Parliament has delegated them that power, etc.

However they remain subordinate to and serve at the pleasure of the House of Commons. At any time the house can make a motion of no confidence and remove the Prime Minister with a simple majority. Certain things such as the budget are an automatic confidence vote--failing to pass a budget means you're dismissed. (Sometimes they're replaced, often this triggers an election to, excuse the pun, give voters an opportunity to get their house in order.)

They're not dramatically limited relative to the US President, but their position is a lot more tenuous and requires ongoing support from government for them to remain in power. Instead of shutting down the government if the prime minister can't put a budget together, we just fire the prime minister. Instead of doing a split-brained thing where two parts of the government get deadlocked, we just fire the prime minister.

What happens if the House of Commons goes crazy? Canada has a Senate. It's 105 members that are selected by appointment. They serve until age 75. They're generally unaffiliated with any specific party. There are actually some women there (~55% versus ~30% in the house). The members are selected by whoever is in power at the time of a vacancy, however it's not generally treated as partisan (and steps are being taken to make it explicitly non-partisan). Over time, though, it would tend to follow larger election/political trends. Since it's a "lifetime" appointment, the Senate can act against populism and as a damper to pull the government towards status quo.

The Senate is described as the chamber of "sober second thought" because anything the House of Commons passes has to be passed by the Senate to become law. It's rare for something to pass the house and not the senate (some notable examples being things like an attempt to criminalize abortion), however I'll say with no basis that that doesn't mean they don't have influence--the house is unlikely to try and send anything up to the senate that they have an indication would be rejected.

And if the Senate goes crazy? We left an escape hatch--constitutional amendments are not voted on by the Senate. The House of Commons can pass a constitutional amendment which has to be approved by the provincial assemblies in at least 7 (of 10) provinces collectively representing at least half of the population.

So to boil that rambling mess down--

The Legislature is essentially trusted with running everything. They delegate power to the Executive which is given wide powers, but the process of taking away that power is made very easy. The check on the Legislature is a group designed to be a lagging indicator and not beholden to anyone that acts as a damper. If anything isn't working, we default to throwing it all out and trying again. We left some escape hatches that involve going back to the people.

We haven't had to deal with the same sort of direct attacks that the US has, but... well, fingers crossed.