1.) Ok, if the history tab in Electrum shows the timestamp of the first confirmation:
Where can I see INSIDE Electrum when I sent initially the transaction to the mempool?
Again: TWO timestamps are required: initial sent (to mempool) and 1st confirmation.
I guess a (new) column "sent time" in History tab is missing. At least optionally
That should be feasible in Electrum.
I don't need absolute exact timestamps. Timestamps +/- 30 seconds would be acceptable.
I agree with you an option to show this data in the GUI interface or at least through the commands in the console is missing and would be welcomed. But if you really need it you can find this information in the logs files of Electrum (until they're deleted at least), the directory of those logs is normally located in the same directory as the one cointaing the wallet directory, but you need to have enabled them first. I hope it could help you.