Short answers, pulled from the story.
The Second Federal Republic of Mexico began on the 22nd of August 1846 when Mariano Salas restored the Constitution of 1824. The republic ended in June 1863 after Maximilian of Habsburg assumed the throne following the fall of Mexico City.
Mariano Paredes held the presidency when the war erupted in April 1846 before resigning on July 28. Manuel de la Peña y Peña assumed the presidency on the 8th of January 1847 after Anaya's term expired while the capital fell to American forces.
Military defeats against the United States fueled public anger that forced President Mariano Paredes to resign on July 28. A revolt by garrisons in Vera Cruz and San Juan de Ulua installed Mariano Salas as provisional president who restored the Constitution of 1824 on August 22.
President Benito Juarez passed a moratorium on foreign debt payments in July 1861 which triggered the Convention of London. France, the United Kingdom, and Spain responded with military intervention that resulted in three navies occupying Veracruz on the 8th of December 1861.
The Constitution of 1857 was promulgated on the 12th of February 1857 after Congress ratified Comonfort's ascension in February 1856. This constitution integrated the Ley Juarez and the Ley Lerdo into law while declaring man's inherent freedom and abolishing special courts for clergy and military.