Short answers, pulled from the story.
The Concordat of 1801 was an agreement signed on the 15th of July 1801 between the First French Republic and the Holy See, negotiated by Napoleon Bonaparte and Pope Pius VII. It restored Catholic clergy from exile and recognized Catholicism as the religion of the great majority of the French, while allowing the state to retain control over bishop appointments and church finances.
First Consul Napoleon Bonaparte signed on behalf of France, and Pope Pius VII signed on behalf of the Holy See. The agreement was signed in Paris on the 15th of July 1801.
The Concordat remained in effect in France until the law of 1905, which separated church and state. In the Alsace-Lorraine region, which was under German Empire control when the 1905 law was passed, provisions of the Concordat remain in force today under the local law of Alsace-Moselle.
No. The Catholic Church formally surrendered all claims to lands confiscated after 1790 as part of the Concordat's terms. Those properties, which had been sold off during the Revolution, were not returned.
Napoleon appointed his brother Joseph Bonaparte, counselor of state Emmanuel Cretet, and theologian Etienne-Alexandre Bernier. Pope Pius VII's team included Cardinal Ercole Consalvi, Cardinal Giuseppe Spina (Archbishop of Corinth), and theological adviser Father Carlo Francesco Maria Caselli. French bishops had no role in the negotiations.
The Organic Articles were a set of companion laws Napoleon presented alongside the Concordat, promulgated in April 1802. According to historian Georges Goyau, they infringed on the spirit of the concordat by extending state recognition to Protestants and Jews as well as Catholics.