You don'e need to add "out" in your sentence. She asked for an extra bed in her room. She asked for room service. For the first sentence you could also say, "She asked for an extra bed in her hotel room." To be more specific of what you're talking about.

For the first question, you'd use "for", not "out". For the second one you need to also omit the "out" - "out" doesn't make sense in any of these sentences.

Ask out means to invite someone to something, such as dinner, the theater, or a date. (http://www.dictionary.com/browse/ask-out?s=ts) If you want to "ask" somebody "for" something then you will need to use "ask for". The second sentence will be correct if you change it to "She asked for room service". ;)