Multiple trips included
During those 2 years you can travel to the UK as often as you like, as long as each stay does not exceed 6 months.
You do not need to apply again for each trip.
With a new passport
The authorisation belongs to the passport it was granted against. If you renew your passport, you must apply again, even if validity remains.
Finding the date again
The date is in the approval email. If you no longer have it, look up the status using your passport details.