I don't seem to be able to find all the menu options such as adding bookmarks or adding to reading list etc when I touch the book symbol on Safari. It just lists all the bookmarks. What could I have missed?
Touch the share sheet icon (square with an emerging arrow to the right) next to the URL field. What you're looking for should be in the bottom row of icons on the share sheet.
You can't use the book icon to add something to your reading list. You tap the icon you use to create bookmarks, but instead of choosing "Bookmarks", tap "Add to Reading List":
To find your reading list, tap the book icon, and then the glasses:
When you are in the Reading List, press on a line and swipe to the right. You'll get a red "Delete" button and after pressing it, that particular item will be gone. Like this: