die Frage
question
A sentence or formulation used to ask for information or an answer.
Darf ich Ihnen eine Frage stellen?
May I ask you a question?

question
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question
A sentence or formulation used to ask for information or an answer.
Darf ich Ihnen eine Frage stellen?
May I ask you a question?

'Die Frage' (the question) is the noun that belongs to the verb 'fragen' (to ask). If you know the verb, you can easily infer the meaning of the noun.
Er fragt, ob er eine Frage stellen darf.
He asks whether he may ask a question.
In German, you 'stellt' a question: 'eine Frage stellen' (to ask a question). You 'gibt' an answer to it or 'beantwortet' the question: 'eine Antwort geben' (to give an answer), 'die Frage beantworten' (to answer the question). You can also 'eine Frage haben' (to have a question).
Der Journalist stellte dem Politiker eine kritische Frage.
The journalist asked the politician a critical question.
When 'Frage' (matter/question) describes a topic or matter, it often appears in the genitive with an abstract noun. Typical phrases are 'eine Frage der Zeit' (a question of time), 'eine Frage des Geldes' (a question of money), or 'eine Frage des Prinzips' (a matter of principle).
Ob wir in den Urlaub fahren, ist vor allem eine Frage des Geldes.
Whether we go on vacation is mainly a question of money.
The expression 'in Frage kommen' means that something is a possible option. The thing that is an option is the subject of the sentence. The expression is often negated.
Ein Umzug in eine andere Stadt kommt für mich nicht in Frage.
Moving to another city is not an option for me.
The expression 'etwas in Frage stellen' means to question or doubt something. It is an active action. The thing being questioned is in the accusative.
Die neue Studie stellt bisherige Annahmen in Frage.
The new study calls previous assumptions into question.
The expression 'außer Frage stehen' means that something is absolutely certain and beyond doubt. The thing that is certain is the subject of the sentence.
Seine Kompetenz für dieses Projekt steht völlig außer Frage.
His competence for this project is completely beyond question.
problem
'die Frage' and 'das Problem' can both refer to something that still needs to be clarified. 'die Frage' sounds more neutral: it is about a topic or point for which you need an answer or decision. 'das Problem' sounds stronger and more negative, because something is difficult or requires a solution. They can be confused when 'Frage' does not mean a sentence with a question mark, but an open matter. A practical tip: you can clarify a 'Frage', but you have to solve a 'Problem'.

Vor dem Wochenende müssen wir noch die Frage klären, wer den Schlüssel bekommt.
Before the weekend, we still need to clarify the question of who gets the key.
Zu Hause hat mein Freund ein Problem mit dem WLAN und kann nicht lernen.
At home, my friend has a problem with the Wi-Fi and can't study.