'Questions' vs. 'Concerns' vs. 'Doubts'

Solution 1:

The use of doubts to mean questions is, AFAIK, Indian and also Spanish and Portuguese. See here for an explanation.

As I said elsewhere, saying "tengo una duda" (I've got a doubt) when putting your hand up is a common way to make a question in class for kids in Spain. It makes me wonder why English views interaction in terms of answering questions whereas Spanish (and Portuguese) sees it in terms of clarifying doubts. :-)

Solution 2:

I saw this answered once, but I can't remember where.

This comes from a term in the school system in India. They use the term doubts when students have questions about something that the teacher has just explained to the class. From this many students get the misconception that doubts can be used like that in other situations, and that it is a synonym to questions.

Solution 3:

The reason doubt is used in the reported phrases, when you would expect concerns can be explained from the origin of the word doubt.

Doubt has origin from Old French doter (doubt, be doubtful; be afraid), which derives from Latin dubitare (to doubt, question, hesitate, waver in opinion). The NOAD reports the origin is the same; the only difference is that for the NOAD the Old French words are douter (verb) and doute (noun).

Other languages use the equivalent of doubt to mean question. In Italian, somebody who talked in a meeting, or during a class can say avete dubbi? at the end of his talk to ask if somebody have questions.
In these languages, the question equivalent to do you have doubts? is used to mean do you doubt you understood what I said? as an invite to ask questions.

Another explanation of using doubt instead of concerns or questions is that the word used in the native language of the speaker is a false friend of doubt.