I use the "Link" command to capture the value that the user entered in a certain field ("Order number"). Is this then valid in all further screens, or only in the current screen in which the "Link" command has been applied?

It is valid only in the current screen. Either you add a "Link" command to all other screen scripts in which you want to capture the "Order number", or you use the notation  "&[::Order number]". This always gives you the last (most recent) value that the user has entered in an entry field "Order number".