If I have a zone 2-3 travelcard on my student oyster but have to pass through Moorgate which is Z1, will I have to pay any additional fare even if I do not tap in or out at Moorgate?
Also, if I already have a Z2-3 travelcard but wanted to change it to include another zone would I be able to do that and pay the difference or would I have to wait until this travelcard runs out and buy a new one including all the zones?
Finally, would I be able to add a 16-25 railcard onto my student oyster or not?
The fares are charged based on what zones you pass through or are assumed to have passed through. Witness the pink readers at various locations (eg Canada Water, Stratford, Blackhorse Rd) that are there so you can tap to show you changed there and therefore did not go through zone 1. A Z2-3 ticket is not valid for journeys that go through, end in or start in Z1.
Tying it all together, if you pass through zone 1 then you will be charged a zone 1 extension fare. You can have more than one travelcard on an Oyster card, but each one has to be for at least two zones and they must join together at adjacent zones. If you just want to add zone 1 then you might be better off waiting. If your travelcard is for a long period then you could try getting an exchange which will cost £5 plus the difference in price for the remainder of the validity. As Alan says, you can add a 16-25 railcard to get discounts on off-peak fares and caps, including extension fares.