Yes, #Primal is a client, or an app if you will, that's built on the noster protocol. Couple of clients/apps are there for Nostr. They all can technically communicate with one another. It's kind of like the email, where you have Gmail, Yahoo mail, etc. and you can send email from one to another.
About flagging content, yes, you can mute or block any content or user you don't want to see. But I'm afraid, it's just client or app specific. Meaning, if you mute or block something or someone on Primal, it might not be transferable across other clients or apps, like on Amethyst for example.
About content moderation, some clients have some block lists for some content types or some relays even filter which types of contents they will allow.
But it's mainly it's up to the user to block/mute the content they don't want to see.