there is an excellent Passenger Assistance app (lower case rounded green "p" icon) which has all the features of the online version plus some.
Hampton Court Palace, from the Hampton Court station is easy. The trains are not quite level with the platform so you can have a ramp, but the whole station is level. Out the front, turn right directly over the Thames, turn right again and you are there. Hampton Court is the end of the line so you have plenty of time coming and going.
Hampton Court Palace has a very good accessibility page (not always easy to find that page - here it is https://www.hrp.org.uk/hampton-court-palace/visit/accessibility/ , telling you where the hidden lift is in the Palace, and extraordinarily helpful uniformed Hosts and Volunteers with sashes. They have always taken excellent care of my wife.
The main entrance to Waterloo Station is up many stairs (very Victorian) but there is a level way in.
There are two train routes to Windsor Castle (I presume when you say just Windsor you mean the Palace, not wandering the town??). The line from Waterloo to Windsor and Eton Riverside has a couple of advantages for a wheelchair user - no changes are required and it is a little cheaper. On the other hand, that route is slower, goes from Waterloo (more or less convenient depending on your hotel) and worst of all, Windsor & Eton Riverside is, as you might guess from the name, at the level of the river so there is quite a slog up a relatively steep (for disabled users) hill around the outside of the Palace and at the top you are at the entrance.
The other route is to Windsor & Eton Central which is on the same level as and directly across the road from the Palace entrance. The traditional route would start at Paddington station, change at Slough and hop on the little shuttle train which runs around to Windsor & Eton Central. Rail staff assigned by Passenger Assistance will help you off the train from London and onto the train to the Palace. In addition to the GWR service from Paddington, the London to Slough segment is also served by the Elizabeth Line from many London stations. The Elizabeth Line looks like a tube line but it is actually a real train and covered by Passenger Assistance. In TfL stations it will be TfL staff.
So advantages of Windsor & Eton Central - available from central London as well as Paddington, level access from the station to the Palace, faster. Disadvantages - the change at Slough (assistance available) and slightly more expensive.
I've never traveled to Canterbury by train so I will let others speak about the accessibility. I will say that if you choose the High Speed train from St Pancras it is one level up with convenient elevators, and faster but more expensive than from the conventional train stations, a huge number of restaurants and other services in St Pancras and very wheelchair friendly.
