1. Yes, she can do this! While the disruption to the fog will be temporary, it's possible to dispel it for brief periods or reduce its thickness which will help find survivors. She may find that doing so requires more effort than she's used to as if she's contending with a power greater than mere weather. She will have no trouble manipulating the waters.

2. She can try, but that's correct, for the sake of continuity, she won't be able to succeed. However, her meddling will cause the lighthouse's lightbeam to swing in her direction and she will get the distinct sensation that she's been "seen." Thorne would also be grateful for her efforts regardless.