Hi Anu,
You can definitely use TM or EM to get the events but as you said you have additional data associated with events, I would say go with EM extraction using the FMs I mentioned.
As with question of replicating the events to TM, I would say you should still replicate to TM as the execution data is readily available against TM documents in execution tab and might help you with overall execution status of TM documents. Secondly, it would be your business decision to replicate the events or not 
Thanks,
Vishnu