Short answers, pulled from the story.
The Tolkien Estate sent a cease and desist to TSR, the original publisher of Dungeons & Dragons, requiring the removal of the name "hobbit" from all official materials. The name "halfling" replaced it. The original 1974 edition had introduced the creature as a player character class under the name "hobbit," drawn directly from J.R.R. Tolkien's fiction.
The earliest subraces, introduced in the 1977 Monster Manual, were the hairfoot, the stout, and the tallfellow. Later editions added the lightfoot, deep halfling, ghostwise, and strongheart variants. The 2004 Unearthed Arcana catalogued aquatic, arctic, desert, jungle, and water halflings, and the 5th edition Player's Handbook (2014) settled on the lightfoot and the stout as its two default subraces.
Yondalla is the chief halfling goddess and the race's creator deity in D&D lore. She was created by James M. Ward for the Deities and Demigods Cyclopedia in 1980 and is depicted as a strong female halfling with red-golden hair, carrying a shield with a cornucopia motif. She is worshipped in two aspects: the Provider, who governs fertility and growth, and the Protector.
The kender is a distinct race in the Dragonlance campaign setting that takes the place usually held by halflings. Kender are completely immune to fear, including magically generated fear, and they regard taking other people's possessions as borrowing rather than theft.
In Eberron, introduced in 2004, halflings are nomadic, clannish barbarians who ride domesticated dinosaurs as mounts across their prairie homelands. Other races view them as barbarians, though they can integrate into human cities when they leave the plains. Some settle in cities permanently while retaining strong ties to their cultural heritage.
Regis is a halfling rogue and member of the Companions of the Hall, the adventuring group led by Drizzt Do'Urden, in a series of Forgotten Realms novels. He carries a crystal pendant that can charm people. In the final battle of The Crystal Shard, published in 1988, he saved the day in a manner that critics compared to Bilbo Baggins.