Confusion regarding regular language
The statement (2) is ambiguous. It could mean either
$$
L \text{ is regular but } L \text{ is not equal to } 0^+ \tag{1}
$$
Or it could mean,
$$
L \text{ is regular but } 0^+ \text{ is not regular} \tag{2}
$$
(1) is true and (2) is false.
The authors of the question intended it to mean (1).
But you thought that the meaning was (2), so you were confused.