Given that no one really came forward with an answer, I am going to answer my own question. I am writing this answer at the Star Alliance Business Class lounge at departures so this experience is fresh.
My original questions
Is it an issue that my transit time is longer than 12 hours? Can I
still leave the airport?
The transit time being longer than 12 hours does not matter. Leaving the airport is still a possibility but in this particular instance, there was an early evening curfew due to the domestic situation in Egypt. Upon arriving at the airport, passengers can request a transit visa (bear in mind, citizens of certain countries cannot obtain a visa on arrival). The processing of the visa takes about an hour and you can then leave the airport.
What are my options with regards to airport hotels, etc.?
EgyptAir arranges complementary hotel stays for passengers with transit times greater than 6 hours. This hotel stay is optional. In other words, you can either take a transit visa and leave the hotel OR go with the complementary hotel stay OR just hang out at the airport. Bear in mind, if you choose the hotel stay, the immigration office at the airport will keep your passport and boarding pass and these will be returned to you once you are brought back from the hotel. Transfers to and from the hotel are also provided by the airline. During this visit, EgyptAir brought us to the Le Meridien in Heliopolis.
Any other recommendations about how I could best utilize my time while
in Cairo?
At the time of my arrival from Mumbai in to Cairo, there were several other flights that had just arrived too with passengers who have long transit times. My transit time was about 12 hours so this is how things panned out:
- 1 p.m. Arrive in Cairo and hand in my passport to be able to visit the hotel
- 2 p.m. Processing and collection of all passengers is complete. Start to proceed to the hotel.
- 3.30 p.m. Arrive at Le Meridien Heliopolis. It took long because one of the shuttle buses was full, so we had to wait for the next.
Check in at the hotel took a good 20 minutes too.
- 5 p.m. Wake up call from the hotel to get ready to take the shuttle back to the airport at 6.pm. This is because there was a country wide
curfew at 7.pm.
- 6 p.m. Start boarding shuttle and reach the airport by about 6.45 p.m.
As can be seen, I didn't get much of a chance to catch a nap at the hotel. However, it was nice to be able to drive around and see a little bit of the city.
I hope this helps everyone transiting in Cairo :)