Yes. You can buy tickets online or when you arrive. Make sure you check closure times before you travel.
Easy peasy, all you need to know about the castle is here https:/…windsorcastle
Trains from either Paddington or Waterloo- the latter without changes but slower see www.nationalrail.co.uk
Take a walk along the river, cross over to the Eton side, turn left and cross the Brocas. It makes for a pleasant afternoon, especially if the sun is shining.