1. When he was trveling by train, he met the girl.

2. Being traveling by train, he met the girl.

3. Traveling by train, he met the gril.

(Are the three sentences correct and the same?)

No, they're not.

1 is the best of the three, but correct the spelling of "traveling" please!

2 is not grammatically correct.

3 is OK, but correct the spelling of "girl."