Short answers, pulled from the story.
The earliest documented ancestor is Heinrich Motzhardt, who lived from approximately 1320-1350 to 1400. The family name appeared in records from the Bavarian part of Swabia, spelled "Motzhart" or "Motzhardt" in the earliest documents.
Mozart had six children with Constanze Weber, four of whom died in infancy. The two who survived were Karl Thomas Mozart (1784-1858) and Franz Xaver Wolfgang Mozart (1791-1844). Both sons died unmarried and childless, ending the direct bloodline.
Johann Georg Leopold Mozart (1719-1787) was a court musician and violin pedagogue, and Wolfgang Amadeus Mozart's father and primary teacher. He married Anna Maria Pertl (1720-1778) and is credited with recognizing and training his son's exceptional talent.
Carl Maria von Weber (1786-1826) was connected to the Mozart family through his uncle Sebastian Mayer (1773-1835), who married Josepha Weber (1758-1819). Josepha was the sister of Constanze, Wolfgang Amadeus Mozart's wife, making Carl Maria von Weber a collateral relation by marriage.
Several generations were craftsmen in Augsburg. The family included farmers in Pfersee, master masons, bricklayers, a guild master who built the provost's church of St Georg in Augsburg, and bookbinders. Franz Mozart (1649-1693/4), Wolfgang's great-grandfather, was a master mason.
Yes. Maria Anna Mozart, known as Nannerl (1751-1829), married Johann Baptist Franz Berchtold zu Sonnenburg (1736-1801) and had children. Through her son Leopold Alois Pantaleon Berchtold zu Sonnenburg (1785-1840), she had grandchildren including Bertha Forschter (1842-1919), who lived into the twentieth century.