I can't change the number value in the numbered list. After typing the needed number in the Restart numbering at, the needed number isn't changed.
Have you entered any text in the list item?
Have you pressed Enter?
Yes, I pressed Enter and typed some text.
In the Authoring area you pressed Enter to start the new list item and entered some text. When you changed the number in Properties to 3 did you then press Enter there?
Yes, I pressed Enter when I changed the number in Properties to 3 did
Your image shows the item is a paragraph rather than a list item.
Your screenshot shows a p is selected rather than an li. I wonder if you have Autonumbering set up, rathar than lists.
I've never used it, but from a quick test, if you are, I think you need to click in every paragraph and check what number is configured for each paragraph. Delete the number for every paragraph where you don't want a custom number.