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Is there a way to get an estimation of how many transactions are being currently (last hour or last 24h) processed by the lightning network? And by a specific node?

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Yes, that is possible. If you operate all nodes in the network :)

If you are interested in a specific node, performing an effective sybil attack will also allow you to determine number of transactions which are routed through or initiated by that specific node.

Other than that, there is no way to accurately determine transaction rate of the network, as only channel capacity is publicly broadcast.

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No. You can only estimate some bounds on that number, but they will be nowhere near reality. You can only say how many transaction your node processes. But you cannot say anything about other nodes, unless you are participant in all of their channels as well (or at least some, to get better bounds estimations). So, you can ask the node owners to give you that information. But they can lie to you. It is also unlikely that many owners would share such an information to protect their privacy.

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