I think they are mostly used as "wondering aloud": you are not sure, so you are asking yourself.
As you quoted, "이렇게 하면 맞을라나?" would be "I wonder if this would be right?" Other examples I can think of:
선생님이 화내시려나? = I wonder if the teacher will get mad?
(Kind of a cliche) 아이구 허리야, 비가 올라나... = Ouch, my back hurts, is it going to rain...
(It used to be common that many elder Koreans had chronic back pains which became worse with high humidity, just before it rained.)
You could use the form to actually ask a question to someone else, but in that case it will be considered 반말, so you can't use it in a polite setting. (You can add -요 to make it more polite.) Compare:
선생님이 화내시려나? (반말: to a friend)
선생님이 화내시려나요? (해요체: somewhat polite)
In such a case, I think it is more common to use -ㄹ까 or similar forms:
선생님이 화내실까? (반말)
선생님이 화내실까요? (해요체)
선생님이 화내실 것 같습니까? (very polite)