How to determine how many transactions are being processed by the lightning network? 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?
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.