Praise be to Allah, and peace and blessings be upon the Messenger of Allah and his family.
It is not permissible to give prizes, whether in the form of money or otherwise, except in the case of camel races, horse races or archery contests, according to the majority of scholars. Some scholars added to that competitions in memorizing the Quran , Hadith and Fiqh, and whatever can help in promoting Islam.
The basic principle regarding that is the report which was narrated by Abu Dawud (2574), At-Tirmidhi (1700; he classed it as sound) and Ibn Majah (2878) from Abu Hurayrah (may Allah be pleased with him), from the Prophet (blessings and peace of Allah be upon him), who said: “There should be no prizes for contests except in archery, horse races or camel races.” (Classed as authentic by Al-Albani in Sahih Abu Dawud, and others)
As-Sindi (may Allah have mercy on him) said:
“Al-Khattabi said: That is, it is not permissible to accept money as a prize for contests except in these two cases, namely camel racing and horse racing. We may add to that similar contests, such as contests in using tools of war, because awarding prizes for that is encouraging Jihad and motivating people to participate in it." (Hashiyat As-Sindi ‘Ala Sunan Ibn Majah 2/206)
It makes no difference whether the prize comes from the wealth of the competitors themselves or from the wealth of some external party.
All of that is prohibited except in the three cases mentioned above, and anything that comes under the heading of supporting Islam may be added to that.
But if the price comes from the wealth of the competitors themselves, then it is gambling ; if it comes from the wealth of others, it is not gambling, but it is still prohibited, because it comes under the heading of a prize that is forbidden.
In most cases, such competitions have to do with things that are not useful, and may even involve things that are prohibited, such as music and the like, and it is not permissible to spend money on prohibited things. The wise person only spends his money on things that are beneficial. So this is another reason to prohibit these contests.
Shaykh Al-Islam Ibn Taymiyyah said:
“If the prize is given by one of the contestants, or by an outsider, then it is a kind of award, yet it is forbidden, except in the case of things that are beneficial, such as horse and camel races and archery, as it says in the Hadith: “There should be no contests except in camel races, horse races or archery.” That is because spending money on that in which there is no religious or worldly benefit is forbidden , even if it is not gambling." (Majmu‘ Al-Fatawa 32/223)
Based on that, it is prohibited to give prizes for competing in such challenges, even if the prizes come from the audience.
For more details, please see the following answers: 14220 , 114530 , and 89743 .
And Allah knows best.