I always find the terminology strange.

If there is only one party permitted, and that one party is supreme, then how is that a party? It looks like government to me. Maybe the translation to English is just wrong. The "party" isn't a party by any reasonable definition.

The real parties would be factions within the so-called party. I don't know if they have names more descriptive than "Xi supporters" and "Xi opponents".

US institutions also answer to the US government...

Judges don’t answer to the government. They can be impeached, but that effectively never happens.

So they answer to no one?

We trust them to answer to SCOTUS, who we in turn trust to interpret the constitution that a majority of us have agreed to keep. Basically a group of people whose entire job is to interpret the actions in terms of law, constitution, and human rights - a marrying of theories on social contract, natural rights, and separation of powers that we've seen emulated (and improved upon) across the free world :)

Overall, I particularly enjoy this system over one that is accountable to a single entity.

They can be overruled by higher courts, and in some localities they’re forced to run for election.

Yes, and those leading the government are elected by the people every few years.