Can minors apply for a visa on their own to travel to South Korea for a K-Pop training program?

The official visa page of the South Korean embassy in Tunisia doesn't mention such a restriction, however it's likely that they will ask you for a signed permission from your parents as it's standard policy of most consulates worldwide.

Regardless of the visa requirements, you should be extremely careful about offers from abroad that sound too good to be true. There are hundreds of thousands of teenagers in South Korea itself who would love to enter a "K-Pop training program", so I'd be very suspicious if someone invited an underage person for a "chance to become an idol". If you do plan to go, please double check with your parents and then double check with the Korean consulate if the program is actually legitimate. You do not want to end up in South Korea as a victim of human trafficking, so please apply serious scrutiny before you leave.

Does a minor need a parents permission to apply for a visa and to travel unaccompanied to another country?

Absolutely. Example for Canada

If a minor child is travelling alone

The child should present:

a letter of authorization, in English or French if possible, and signed by both parents or by their legal guardian which lists: the parents’ (or legal guardian’s) address and telephone number, and the name, address and telephone number of the adult who will look after the child in Canada.

United Kingdom

You can travel to the UK without an adult (someone over the age of 18).

Your parent or guardian will need to provide their:

written consent for you to travel to the UK

South Africa a Parental Consent Affidavit is required, here is a Sample. And so forth.

Most airlines won't accept a minor child (although the age for that varies) without parental consent either.

Do you have your passport already? The majority of countries require a parents signature for a minor to apply for the passport. And showing up without them, with an already signed application, will likely be refused as there is no way to prove your parents actually signed the document.

Can you apply for a visa without your parents? You need to call the South Korea Embassy to find out their rules on issuing visas to minors. Each country's regulations vary and those rules can even vary from consular location to consular location (ie rules for Korean visas issued in the UK can be different than rules for Tunisia).

Can you leave the country and fly without your parents? You need to confirm rules with the airline you plan to fly on out of Tunisia what their rules are for boarding minors on international flights. You also need to confirm with the South Korean Embassy what rules apply to you when you actually enter the country (assuming they issue a visa). It is highly likely you will need at a minimum a notarized letter from your parents authorizing you to travel without them (which means your parents WILL need to go to the municipal offices or other offices authorized to notarize / certify a signature).

But one has to ask, since your parents seem unwilling to help you with your procedures, do you actually have their permission to do this?