Short answers, pulled from the story.
French forces under Marshal Davout crossed the Wkra River to attack Russian positions near the Bug-Narew confluence. The 17th Light Infantry Regiment and cavalry units drove Ostermann-Tolstoy's troops out of Czarnowo before they recaptured the village.
Field Marshal Mikhail Kamensky led the Russian army in Poland while Generals Levin August Count von Bennigsen and Friedrich Wilhelm von Buxhoeveden commanded its wings. Lieutenant General Nikolay Tuchkov, Lieutenant General Dmitry Dokhturov, Lieutenant General Peter Kirillovich Essen, and Lieutenant General Heinrich Reinhold von Anrep led specific divisions within Buxhoeveden's wing.
Historian David G. Chandler estimated total losses as 1,400 men on both sides while Digby Smith asserted French casualties were 16 officers and 830 men with Russian casualties totaling 41 officers and 1,360 men plus five captured guns. Ostermann-Tolstoy admitted losing 500 men but Alexander Mikhailovsky-Danilevsky stated that 853 Russians were killed and wounded including three generals.
Napoleon decided to secure a position on the east bank of the Vistula River before winter weather forced a stop to campaigning. The battle occurred near the point where the Wkra emptied into the Bug-Narew river system east of Warsaw.
Napoleon ordered his brother Jérôme Bonaparte to protect his southern flank by operating against Glogau in Prussian-held Silesia. He wished to deny Warsaw to the approaching Russian army and secure a position on the east bank of the Vistula River before winter weather forced a stop to campaigning.