She may have been hanging out with Vandene and Adeleas. They live in Arafel which borders Shienar. Or maybe she was telling people exactly where the waygate is to shut it down. We know she learned balefire between the end of EotW and the end of tDR, and she was very busy during tDR, so it was during one of her trips that we didn't see.
That is what I think to be most likely, but it's still pretty sketchy. The timing was rather coincidental.
The Forsaken thing has been explained. Sammael didn't bother to guard his dreams, so it was obvious to Moiraine when everyone was having the same dreams. I can't remember what the other hints were but they were there.