All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger.
That teacher (whom the question refers to as a 'private answer individual' is neither obliged to answer all the questions of that learner, nor to solve all his problems, except in case he asks him about knowledge that he needs regarding his religious obligations, and not in regard to optional matters of knowledge.
These details were provided by the scholars when interpreting the hadeeth reported by Abu Daawood, who related that Abu Hurayrah, may Allah be pleased with him, narrated that the Prophet said, “The one who is asked about knowledge (of the religion) and conceals it will be bridled with a bridle of fire on the Day of Resurrection.” Al-Khattaabi said:
“This is in regard to the knowledge that is obligatory, such as when someone sees a non-Muslim who wants to embrace Islam and says: ‘Teach me Islam? What is the religion? How do I pray?’ And like someone who comes to ask about what is lawful or unlawful. In such cases, they must not withhold the answer to what they were asked about, as withholding it results in the threat and punishment (mentioned in the hadeeth), but this is not the case in matters of optional knowledge which people do not need to learn as a necessity.”
There is another case in which it is not obligatory to answer the questioner about what he asked for, or to teach him, which is when there are other people of knowledge available.
An-Nawawi said in Al-Majmoo’, “Issuing fatwas is a communal obligation; if a scholar is asked for a fatwa and there is no one else to issue fatwas in his region, then he is obliged to answer. If there is someone other than him who he is present [and available], then giving an answer in regard to both of them is a communal obligation. In case there is someone other than him but he is not present, then there are two views: the most correct opinion is that it is not obligatory (he is not obliged to answer), as has been stated previously by Abdur-Rahmaan ibn Abi Layla… ”
Here, Imaam An-Nawawi refers to the statement of Abdur-Rahmaan ibn Abi Layla, who said, "I met one hundred and twenty of the Ansaar who were the Companions of Prophet Muhammad and there was no one of them who spoke about knowledge except that he had wished that it was his brother who had spoken instead of him, and there was no one amongst them who issued a fatwa except that he had wished that it was his brother who had issued it.”
Nonetheless, a scholar should be patient for the sake of teaching knowledge to an ignorant person, as there is much reward in doing so. Also, the one who asks for knowledge should have good conduct with the person he asks knowledge from.
Allah knows best.