Short answers, pulled from the story.
The Third Battle of Kharkov ended on the 15th of March 1943 when German forces declared the entire city back in their hands. Fighting continued block by block until this date after the SS Division Leibstandarte launched a two-prong attack into northern Kharkov early morning the 11th of March.
Field Marshal Erich von Manstein commanded the German counterattack against Soviet forces during the Third Battle of Kharkov. He flew to Zaporizhia to meet Adolf Hitler on the 19th of February 1943 and received operational freedom to deploy fresh units including the II SS Panzer Corps.
Manstein's forces had approximately 350 tanks available at the point of contact during the Third Battle of Kharkov. This number outnumbered Soviet armor almost seven to one despite earlier reports that armored forces dwindled to fewer than 500 operational tanks along the entire front.
The Red Army suffered over 80,000 personnel casualties during the Donets Campaign which included the Third Battle of Kharkov. Of these troops 45,200 were killed or missing while another 41,200 were wounded between the 13th of January and the 3rd of April 1943.
Bevin Alexander called the Third Battle of Kharkov the last great victory of German arms on the eastern front. Military historian Robert Citino described the operation as only a brief glimpse of victory rather than a strategic triumph due to the cost in manpower and equipment left Germany vulnerable to future Soviet offensives.