Short answers, pulled from the story.
The War of Laws was a series of conflicts between the central Soviet government and the governments of the Soviet republics from 1989 to 1991. Republics passed laws asserting sovereignty over their territories, Moscow declared those laws unconstitutional, and the republics refused to recognise Moscow's rulings. The deadlock contributed directly to the dissolution of the Soviet Union.
Estonia was the first Soviet republic to declare sovereignty, doing so in 1988. All fourteen other republics followed by 1990.
The Soviet Union officially ended with the signing of the Belavezha Accords on the 8th of December 1991 between Russia, Ukraine and Belarus. The accords established the Commonwealth of Independent States as a successor body, and Gorbachev resigned from the Soviet presidency later that month.
Tatarstan declared itself an independent state in 1990, claimed ownership of its oil reserves, and severed ties to Russian law and taxes. Under Vladimir Putin, Tatarstan became the leading region pushing for "official asymmetry" before being compelled to rewrite its constitution to reflect closer ties with Moscow.
On the 10th of November 1989, the South Ossetian Autonomous Oblast requested elevation to Autonomous Soviet Socialist Republic status. The Georgian SSR and the central Soviet government could not resolve the legal dispute, and the conflict escalated into the South Ossetian War, becoming one of the region's ongoing frozen conflicts.
Yes. After the Soviet dissolution, Yeltsin encountered a new War of Laws with the Russian Parliament, which blocked his legislative agenda. He signed the Federal Treaty to win regional support and created the Russian Constitution to extend powers to republics affiliated with Russia.