Short answers, pulled from the story.
Star Wars: The Empire Strikes Back for the NES is an action-platform game based on the 1980 film. Players control Luke Skywalker through stages set on Hoth, Dagobah, and Cloud City, eventually rescuing Han Solo and defeating Darth Vader in combat.
The game was released in 1992 for the Nintendo Entertainment System. It was a sequel to a Star Wars NES game released the previous year.
The film ends with Han Solo frozen in carbonite and no decisive confrontation with Darth Vader. The game requires the player to both rescue Han Solo and defeat Darth Vader in combat to finish.
On the 26th of July, 2019, Limited Run Games re-released both the NES and Game Boy versions in limited quantities on unlicensed replica cartridges, with approval from Disney and Lucasfilm. Both standard and Collector's Edition sets were produced.
Glenn Rubenstein of Wizard magazine praised the game's plot faithfulness but called the fighting and platforming tedious, writing that "the more diverse sequences more than make up for it." A reviewer in Power Unlimited called it "a fun game, although the worlds are very similar."
After completing The Empire Strikes Back for NES, the development team moved on to making Super Star Wars for the Super NES. As a result, no NES adaptation of Return of the Jedi was ever developed or released.