I'm not sure about the first question. I would say the correct use of 'either' is always with 'or'. Do you have a specific example of either being used alone? As for the second question: 'rather than' can be used as 'intead of'. So: "I would choose this instead of this" = "I would choose this rather than this". Also you can use 'rather' with the meaning of 'quite', as to underline an adjective. 'It is rather beautiful' = 'it is quite beautiful'. Hope this is helpful :)

In conversational English, either is used much more often. Either indicates the choice between something and something else. Example: "You can have either tea or coffee, which would you like?" Rather indicates something to replace something else. Example: "Would you rather have tea instead of coffee?" In English, we seem to use shortcuts to get the point across though. Examples: "Do you want tea or coffee?" (The word "either" would have been used.) "Do you want tea instead of coffee?" (The word "rather" would have been used.)

About either, the only times I see it without or, is when the options are assumed, or they are expressed in the question, like when somebody asks: Do you want to do A or B? you can answer with, I can do either one. Do you have any examples of when you see either without or? "Than" implies a comparison: Something has less or more of a quality "than" something else. "Rather" implies a preference, or a statement of something having much of a quality than unexpected. In the first case, you could say: I rather do A, or: I rather not go. In the second case, you could say: this is rather surprising, or this car is rather fast. Hope this helps