London City Travel... Bus/Trains/Tube?

Yes the Underground and the Tube are the same rail transport system in London. Do not confuse this with the Overground. The Oyster Card works on both the Tube and Buses. Buses do not take cash anymore so you will need either an Oyster Card or a cashless debit or credit card.

Yes and Yes.

Your best option, at least in my opinion, is the Oyster card. No zones to worry about, the Oyster tracks that for you. You just buy an Oyster and load some pounds on it and travel until it says you need more funds. You will never pay more than the maximum capped amount a Travel card pass would cost you but instead of paying for zones you may never actually enter by guessing about what coverage you need, the Oyster takes care of that. When you leave London, you can cash in your Oyster at a tube station ticket machine and it will pay you back in cash up to £10 plus the deposit for the Oyster. Or you can hold on to your Oyster for your next visit as the funds do not expire.

Can I purchase the card and reload it at a station using cash? That way i don't have to encounter an international transaction fee.

"Can I purchase the card and reload it at a station using cash?"
Yes.
BTW, the oyster card can also be used on the Docklands Light Railway (DLR).

Buying an Oyster Card or refilling it with more money, ie say only 5GBP are left on it, you have a choice of using a credit card or cash. Some machines take only cash, some take both and some take only credit cards.

I use the Oyster card in London, very convenient on buses and the Tube, I recharge it before flying back here so that the next time in London the card will be ready.

I’m looking forward to using the Oyster card I bought last trip when I’m in London 3 weeks from now. As mentioned, they are accepted on buses.

The nice thing about buses is you get to see the city. The bad thing about buses is they get stuck in traffic, especially during rush hour and in the heart of the city. The Underground avoids the traffic, but you don’t see the town.

Actually, my wife and I walked a lot, averaging 10-12 miles a day (not bad for 60 something geezers). We walked from Selfridges through Green Park, past Buckingham Palace back to Westminster. We also walked from St. Paul’s down the Stand, through Trafalgar Square, past Parliament to our Westminster Hotel.

"Actually, my wife and I walked a lot, averaging 10-12 miles a day (not bad for 60 something geezers)."

My wife and I also walked 10-12 miles per day in London but we are in our mid 70s.

I don’t track daily walking mileage, but the main parts of the city are surprisingly walkable. If some cases, it’s as quick to walk as to take the tube.

Oyster is your best bet - with three far flung destinations of Gatwick, Wembley and Watford Junction where Oyster is accepted to each as well as some central London transport it will work well.

Just remember to tap in and tap out for every journey on the tube and on DLR and trains. If you don't you will be charged the maximum fare because the system doesn't know where you got off.

The two long journeys - to and from Gatwick and Watford Junction for the Warner Brothers will be by train.

Where are you staying in London? It will make a difference in which train you take to and from Gatwick - either Southern to Victoria or Thameslink to various stations further east.

Have you already got your Warner Brothers / Harry Potter tickets? They sell out fast.

Just remember to tap in and tap out for every journey on the tube and
on DLR and trains

Yes - but the buses are different. You only need to tap in, then you pay for the whole route even if you leave at the next stop. Still a better option in many cases.

Edited to add:

Can I purchase the card and reload it at a station using cash? That
way i don't have to encounter an international transaction fee.

Don't you pay a fee on retrieving cash?

You can use the Oyster card to pay for your journey to Watford Junction to see the Potter studios. (You have booked for them in advance, haven't you? If not, do so NOW.)

Actually, my wife and I walked a lot, averaging 10-12 miles a day (not bad for 60 something geezers)."My wife and I also walked 10-12 miles per day in London but we are in our mid 70s.

I have been known to take the tube 10- 12 miles a day and I'm not as old as you.

https://tfl.gov.uk/fares/

Note that some tap-and-go credit/debit cards (with chips) function like the Oyster. All rides for a day result in one charge to the card. There's also a top limit on the Oyster, after which any further rides that day are free.

you can get an oyster card and it works for both underground and buses. i personally prefers buses you can sit on the 2nd level with great views. tube can get really crowded. you can reload money on your card, it can go negative 1 or 2 pounds to give you the last ride.