Problem:
A matter or situation regarded as unwelcome or harmful and needing to be dealt with and overcome.
A thing difficult to achieve or accomplish.
For example, " I've got a problem, i may be late for work. " - Because you may be late that has now become a 'problem' for you.
Question:
A question is when you ask someone something, or something that requires an answer.
The question mark which is '?' symbolizes the sentence as a question.
For example: " Hi, how are you? "
Hope I've helped. :)