In a cavern, in a canyon
Excavating for a mine
Dwelt a miner forty-niner
And his daughter, Clementine
Oh, my darling, oh, my darling
Oh, my darling Clementine
You are lost and gone forever
Dreadful sorry, Clementine
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(Does the front part of the lyric mean #1 or #2?)
1. A miner forty-niner and his daughter, Clementine dwelt in a cavern,in a canyon excavating for a mine.
2. A miner forty-niner and his daughter, Clementine dwelt in a cavern,in a canyon while they were excavating for a mine.
(Q2: Which one is grammatical, 'dreadfully sorry' or dreadful sorry'?)
2 is better, but grammatically it should be "dreadfully." However, many old folk songs pay no attention to grammar rules.
By the way, "forty-niner" refers to people who went to California in 1849 to find gold.
The front part of the lyric can be interpreted as either #1 or #2, depending on the context and the intended meaning.
#1: "A miner forty-niner and his daughter, Clementine dwelt in a cavern, in a canyon excavating for a mine." This means that the miner and his daughter lived in a cavern within a canyon, and they were engaged in the activity of excavating for a mine.
#2: "A miner forty-niner and his daughter, Clementine dwelt in a cavern, in a canyon while they were excavating for a mine." This means that the miner and his daughter lived in a cavern within a canyon, and they were excavating for a mine as a simultaneous action while living there.
Regarding your second question, the correct phrase is "dreadful sorry." "Dreadful" in this context means very or extremely, and "sorry" expresses regret or sorrow. Therefore, the correct expression is "Dreadful sorry, Clementine."