Short answers, pulled from the story.
Westron is the Common Speech of Middle-earth, known as Adûni or Sôval Phârë in Westron, with Sôval Phârë translating to "Common Speech". It was the lingua franca spoken by nearly all peoples within the bounds of the old kingdoms of Arnor and Gondor at the time of the War of the Ring.
Westron is represented almost entirely by Modern English through a pseudo-translation device. Tolkien pretended he had translated the book from Westron into English rather than composing it himself, which explained why the Common Speech appears as English throughout the novel.
Westron developed from Adûnaic, the ancient language of Númenor. Adûnaic was spoken at the Númenórean haven of Pelargir near the Mouths of Anduin, where it mixed with words from local languages to become the Common Speech that spread along the coasts of Middle-earth.
In Appendix F to The Lord of the Rings, Tolkien gives examples including Karningul (Westron for Rivendell), Sûza (Westron for the Shire), Tûk and Bophîn (Westron originals of the hobbit surnames Took and Boffin), and Zaragamba (the Westron original of Brandybuck, meaning "Oldbuck" from zara "old" and gamba "buck").
Tolkien explains that Sam and Ham "were really called Ban and Ran", shortened forms of the Westron names Banazîr and Ranugad. Banazîr was a nickname meaning "halfwise, simple" and Ranugad meant "stay-at-home"; Tolkien rendered them into English using Old English equivalents samwís and hámfoest with the same meanings.
Tolkien used the Mercian dialect of Old English to represent Rohirric because it signaled the genetic relationship between Rohirric and Westron, mirroring the actual historical relationship between Old English and Modern English. This was part of a broader device that mapped the real genetic relations of the Germanic languages onto his fictional language families.