Short answers, pulled from the story.
Daniel received Moscow as an appanage principality in 1263. This small territory likely encompassed the basin of the upper Moskva River, stretching between the eastern influx of the Gzhelka and the western influx of the Ruza.
Daniel defeated Ryazan in 1301 after which Kolomna and Serpukhov were incorporated into the Moscow principality. Pereyaslavl was also temporarily annexed to Moscow, and after Daniel's death his sons seized Mozhaysk in 1304.
Dmitry gathered troops from all territories he controlled and defeated Mamai in the 1380 Battle of Kulikovo. Although later generations saw this Russian victory as a triumph, the principalities remained under Mongol suzerainty until Tokhtamysh sacked Moscow in 1382.
Ivan III succeeded his father and marked the end of the appanage period by gathering the Russian lands into a unified monarchy. He defeated Novgorod in 1471 and again in 1478 when the city surrendered, while Tver offered less resistance before its prince fled to Lithuania in 1485.
A distinct school of icon painting was formed in Moscow in the second half of the 14th century and led by Andrei Rublev. The first original Russian school known as the Suzdal school merged with the Moscow school in the early 15th century.