Why did Padan Fain go to Falme and why did he leave before Rand arrived?
He was trying to gain a power base. His early attempts to do things, were by siding he is trying to get close to someone in power, to influence him. Remember Padan Fain is also Mordeth, and Mordeth was a counselor, Mordeth was a guy who whispered poison in the ear of the king, and had a great deal of power because of it. So Padan Fain has this part of him that wants to influence power and that is what he was doing there. There are these invaders and what rumors says about them is correct.
Why did he leave before Rand arrived, because he must have sensed Rand was near?
Once he could get his hand on the dagger, he wanted out. He didn’t know Rand was coming. Once he realized he wouldn’t be able to have any influence at least, get his hands on the dagger and go, because the dagger is key, the dagger pulls at him.
1) Fain didn’t leave before Rand arrived, and 2) he didn’t get his hands on the dagger.
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