Short answers, pulled from the story.
Boutros Boutros-Ghali coined the term cold peace in late 1982 while serving as a junior foreign minister of Egypt. He later became Secretary-General of the United Nations. He introduced the phrase to describe a situation in which peace existed in name, but efforts to deepen cooperation between populations were limited or deliberately restrained.
A cold war involves states covertly or openly supporting proxy conflicts against each other's allies or client states. Cold peace involves similar levels of mistrust and domestic hostility but stops short of proxy wars, formal incursions, or similar conflicts. A formal peace treaty is in place, though at least one side treats it with vocal domestic disgust.
Egyptian popular support for the 1979 peace treaty collapsed after the 1981 assassination of Anwar Sadat and the 1982 Israeli invasion of Lebanon, and has not recovered since. Contributing factors include pan-ethnic solidarity with Palestinians, religious sympathies, and Egyptian nationalist sentiment against Israel that predates Israel's 1948 independence.
On the 27th of September 1997, eight Mossad agents using fake Canadian passports attempted to assassinate Khaled Mashal, head of Hamas, in Jordan. Two agents injected poison into Mashal's ear but were caught by his bodyguard. After King Hussein threatened to annul the peace treaty, President Bill Clinton intervened and Israel provided the antidote. The Mossad operatives were released after Israel freed 23 Jordanian and 50 Palestinian prisoners, including Sheikh Ahmed Yassin.
King Abdullah II described Jordan-Israel relations as a cold peace in multiple interviews. In a 2010 interview he said relations had reached the lowest point since the peace treaty, and in another interview he described the relationship as "a cold peace that keeps getting colder."
After the Israel-Jordan peace treaty, Israel transferred land near Tzofar, known as Al Ghamr, to Jordanian control but leased it back so Israeli farmers could continue working it. The 25-year renewable lease expired in 2019. On the 21st of October 2018, King Abdullah II announced he would not renew it, and during late April 2020 the land was formally returned to Jordanian control.