Will be in London for 10 days. Plan and getting a 7 day Travel card, I read that it is issued on a Oyster card. After my 7 days has expired can I put an additional 3 days on the Oyster Travel card? Or can I just put money on the Oyster card that was issued as as a 7 day Travel card?
If you put a 7 day Travelcard on an Oyster, if it is a zones 1&2 it will cost you £29.20. Because the off peak 1&2 daily cap on pay as you go Oyster is £7 you will have to use the Travelcard plenty for over 4 of those 7 days. If you only intend to use the Tube and bus from time to time it will be less expensive to have Oyster pay as you go because you only pay for what you use. With a Travelcard on the Oyster you will be unable to get 2 for 1 discounts unless you have other train tickets. Have a look at the Official Price List. That's all by the by though - - - the answers to your question are: 1) No. Travelcards come in 1 and 7 day flavours, not 3. 2) Yes.
If you are travelling solo, I would suggest that you put a zone 1-2 one week travelcard on Oyster plus some pay-as-you-go money (perhaps 10 GBP to start and you can add more). An Oyster card can hold both a travelcard and pay-as-you-go simultaneously. The pay-as-you-go money will cover any trips beyond zone 2 plus your three extra days. With Pay-as-you-go, the daily amount is capped so that you won't pay more than the equivalent one-day travelcard. If you are travelling with someone else, you may want to consider the paper travelcard issued by the rail stations in order to take advantage of the 2 for 1 discounts.
Just a word of warning. Several travelers have reported problems getting an Oyster card refund if they've used a credit card for the initial payment or topping up. If you want a refund at the end of your trip, my advice is to use cash only for all Oyster card transactions.