Do all iMessages always get pushed to Messages on the Mac? Hypothetical situation: Connected on different internet connections. If there are active conversations on my Macbook, and I get a text from one of the conversations not listed there, will it always push it to the macbook? Or if I read or delete it immediately, will it not show on the Macbook? Or are there ways to block certain numbers from going to the macbook?

From what I understand, all messages received will always go to the Macbook if it's configured to do so. There's no way to filter them.

Just wondering how iMessage works exactly.
Unless there is a glitch and as long as you are connected to the internet, you will receive all iMessages that you would get on your iPhone on your Mac. If your iPhone is on the same Wi-Fi network, you will also receive all SMS and MMS texts on your Mac, as well.

If you blocked any numbers on your iPhone, they will be blocked on your Mac and the other way around.

Now, if you receive a text for a conversation that is for whatever reason not on your Mac (like from an internet issue), it should start the conversation on your Mac from that text.