Some of that data, like board actions, are available in Trello's JSON export: https://help.trello.com/article/747-exporting-data-from-trello-1
You might be able to load this into Splunk, but that's not something we've done, personally. You'd need to do this for each board, as there's not a team-level event export, and this won't include any login event details.
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