Is sacrificing with the intention of thanking Allah, or repelling an affliction, or removing an affliction, not legislated? And is sacrificing not an act of worship except in cases of vows (nadhr), sacrificial offerings during Hajj/Umrah (hady), 'aqiqah, and udhiyah? And is anything other than that not permissible except with the intention of charity?

All praise is due to Allah.

Firstly: There is no harm in slaughtering an animal and feeding its meat or giving it as charity, as a form of gratitude to Allah Almighty for a blessing, such as completing the Quran or the arrival of a traveler. This is a righteous deed. Among the ways of showing gratitude to Allah Almighty is drawing near to Him through acts of worship and obedience, including ritual sacrifice (slaughtering for the sake of Allah). Al-Bayhaqi narrated from Ibn Umar that when Umar ibn Al-Khattab, may Allah be pleased with him, completed Surah Al-Baqarah, he slaughtered a camel. Sheikh Al-Islam Ibn Taymiyyah said in his commentary on the verse: "So pray to your Lord and sacrifice [to Him]" [Quran 108:2]: "The intent is that prayer and sacrifice are the noblest means by which one draws near to Allah." Sheikh Abdul Aziz bin Baz was asked: "Does slaughtering fall under the category of charity, and if I want to slaughter to give charity on behalf of the deceased, is this permissible?" He replied: "There is no doubt that slaughtering for Allah and drawing near to Him through it is among the best forms of charity and the best acts of closeness." He also said: "If a person slaughters an animal intending to draw near to Allah and benefit the poor and be kind to them, there is no harm in that." As for slaughtering with the intention of drawing near to the dead, idols, or jinn, it is major shirk (polytheism). It is permissible to give the slaughtered animal as charity on behalf of the deceased or the living, with the intention of drawing near to Allah and seeking its reward.

Secondly: It is not legislated to slaughter what is called "Al-Fadw" (a propitiatory sacrifice) believing that it repels evil and affliction.

And Allah knows best.