Answer and Explanation:
1) TRUTH/TRUE, After a crushing defeat at the Battle of Calderón Bridge on January 17, 1811, Hidalgo fled north, hoping to escape into the United States. He was caught on March 21 and executed by a firing squad on July 30, 1811, at the age of 58.
2) LIE/FALSE, Corralejo de Hidalgo, Mexico was the birthplace of Miguel Hidalgo y Costilla on May 8, 1753.
3) TRUTH/TRUE, The New World refers to the western hemisphere, especially the Americas. The indigenous peoples of the Americas are the pre-Columbian inhabitants of North America, Mesoamerica, and South America as well as Greenland.
4) TRUTH/TRUE, Hidalgo is a Spanish surname.
***About #4, I'm not too sure what you meant by "Peninsular Spanish" but Hidalgo was definitely Spanish. It may be a LIE/FALSE but I wasn't too sure. The other three I understood, though.***
Hope you found this helpful!! <3