Did Song-dynasty China really invent gunpowder, the compass and movable type?

Partly. Movable type was a Song invention, but gunpowder and the compass began earlier in China. The Song dynasty (960 to 1279) is when gunpowder's formula was first recorded and the compass was first used for navigation.

Take gunpowder. It was originally developed by Taoists for medicinal purposes, and the first confirmed Chinese reference to something like it is from the Tang dynasty, in a formula in a text of 808. A later Daoist text describes alchemists who heated sulfur, realgar and saltpeter with honey and got burned hands and faces, even burning down the whole house. The Song dynasty then saw the first surviving chemical formula for gunpowder, in the Wujing Zongyao of the 1040s, and the invention of weapons such as fire arrows, bombs and the fire lance.

The compass began as a fortune-telling tool. It was first invented as a device for divination as early as the Han dynasty, and later adopted for navigation by the Song in the 11th century. The first compasses used for navigation appeared in China by 1088, as described by Shen Kuo. The first compass use recorded in Western Europe came around 1190.

Printing took another step. Around 1040 Bi Sheng invented the world's first movable type printing technology for paper books, made of porcelain. And the Song was the first dynasty in world history to issue true paper money.

The Song thus gave these inventions their first surviving records or uses, and several had earlier roots.