Anyone can run a moderation service. Users subscribe to the services they want. When you flag a post or account for moderation, you choose which service you send the report to.

> How does blocking work?

Blocking works by publishing a "hey I've blocked this person" record in your database. Applications then can use this to enforce that.

> How do people make sure to distance themselves from political enemies?

I'm not sure what this means.

> Do the aggregator cache servers block certain user domains?

They could, and this is also a property that's not really about blocking, that is, you could choose to cache only part of the network if you choose, which could be useful for various reasons.

> How do you ensure that the aggregator returns valid and non-forged comments and likes?

Cryptography, basically.

I'm trying to imagine how a situation analogous to Gab vs Mastodon may arise and play out here, or if the setup is different. Like would they just live side by side, with various frontend aggregators that present one or the other world to you?

> Cryptography, basically.

How do I, the user with a browser verify that? Do I need to use a different client program, or a browser extension? The aggregator site can show me a green checkmark or whatever, but that's just a claim by the aggregator. Am I expected to fire up a terminal window to compute signature validations to check if Alice really put a like on that comment?

You could also use one of the various PDS browser websites to go check their PDS, or a terminal tool, sure. I will be honest and the details of exactly how the cryptography stuff works is not my strongest point when understanding the protocol, maybe someone else can chime in and give you a more detailed description here.