How message propagation works in bitcoin - please somebody help :)

How message propagation works in bitcoin - please somebody help :)

Basically I know how message propagation works in peer-to-peer bitcoin network. But I need a clarification on three points below:

QUESTION 1: In bitcoin network every node relays every message it received to it's peers. If node A received message X and relayed it to his peers, and those peers relayed it to theirs, can we take for granted that finally this message X will return to node A like a boomerang? Because if every node relays every message, it should finally.

QUESTION 2: I know there is no feature in bitcoin client for this, but let's suppose there was one. If node A would like to know if message X was ever relayed on the network, and there would be a feature that allowed to ask it's peers if they had ever received X, and once enough number of peers answered that they do indeed relayed such X, would it imply that all connected (at the time when X was relayed on network) nodes received X? Because if some originator node originates X, than one of his peers relays this X, and their peers also relay X (or at least most of them, which acts honestly), then eventually X should reach all connected nodes, right?

And reversing this, if node A would ask enough number of his peers if they received/relayed X and enough number of them answered that no, they haven't, could node A deduct that X was never relayed on the network, for the same reason as stated above?

QUESTION 4: If theoretically at a given time all nodes participating in the network were connected to network, then a message X send at that time should reach (after some time) all nodes, right?

Please somebody answer this.

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