Short answers, pulled from the story.
Valens was acclaimed as co-emperor on the 28th of March 364 at Hebdomon by soldiers gathered before the Constantinian Walls. His elder brother Valentinian I had been named augustus earlier that year on the 25th of February.
Valens' forces under veteran generals Arinthaeus and Arbitio defeated Procopius at Thyatira and Nacoleia after eight months of fighting. Procopius was executed on the 27th of May 366 following a trial by members of his own escort.
Valens died near Hadrianopolis in Thrace on the 9th of August 378 while fighting Goths led by Fritigern. One account states he was mortally wounded by an arrow, while another describes him dying when Goths set fire to a wooden hut where he sought refuge.
Visigoths crossed the Danube seeking asylum because refugees from Ermanaric's former kingdom could not hold Dniester or Prut rivers against Hunnic invaders. They retreated southward to find defensible lands on the Roman side of the river.
Valens significantly relieved the burden of taxation on the population according to New Catholic Encyclopedia records. Gibbon wrote that Valens diminished oppressive tax burdens instituted by Constantine and his sons while establishing Defensors to guard lower classes.