Just curious if the Citymapper App will help direct us outside the city. Specifically, we want to get to Hampton Court Palace and Hever Castle.
Also, can we use the Oyster cards for these rail tickets?
Citymapper will definitely reach Hampton Court, I would suspect Hever too. Any issues, just use Google map it does 90%+ the same thing. Neither of these is very difficult to find once you are at the nearest station.
Oyster will get you to Hampton Court (zone 6), it won't get you to Edenbridge for Hever Castle.
Hampton Court Palace- yes use Oyster to get there- it's in Zone 6.
Hever Castle- no, you can't use Oyster. You can use your Oyster to East Croydon, but need to buy a new ticket to Hever or Edenbridge Town (turn up and go, no advance fares)- these trains go to Uckfield.
There is no transit to Hever Castle in its rural setting. It's either a taxi from Edenbridge Town or a 1 mile marked walk from Hever.- route map on the Castle website. Hever is an unmanned rural station with no facilities including no taxi rank. If you go there you are walking.
That's the technical answer- you only save £5 or so by splitting the fare on East Croydon. Probably best just to book from London Victoria and stay on the train.