Mariupol is in the Southeast part of Ukraine, along the Sea of Azov. The Russians have not pulled out and are in fact reinforcing the area with units that pulled out from Kiev that is near the Northern central part of Ukraine near the border with Belarus.
Mariupol is in the land corridor that the Russians are trying to establish from the Crimea to the Donetsk/Luhansk area in the far east of the country. Mariupol is the city where the mayor says they have over 10,000 civilians killed. It has been cut off and under siege since the beginning of the war and has been reduced to near rubble by Russian artillery, rocket and missile fire.
The use of chemical weapons mixed with tear gas has been alleged as well as the use of white phosphorus (WP) weapons. There is some disagreement on whether Tear gas and WP are considered chemical weapons...one is a common riot control agent and WP was in common use in WWII/Korea and many other conflicts since.
Ukraine is a large country with unfamiliar names to most Americans. Looking at one of the many maps with illustrations of the combat that is going on would go a long way to understanding what is going on.