Arwen vs. Galadriel

[elbenprincess]

Elves could broadcast their thoughts only if they intended to communicate them

Yes if they intended, Sauron surely didn´t intended that, but what if she was able to do it by force? Her power coupled with her ring? Was Sauron inhernetly that strong at the time, I rather think it was his army that made him so strong.
Still Galadriel was able to read the minds of the fellowship and they didn´t intended that, they not even would know how this works.

I say to you, Frodo, that even as I speak to you, I perceive the Dark Lord and know his mind, or all of his mind that concerns the Elves. And he gropes ever to see me and my thought. But still the door is closed!'

Why would he try to see her thought if he would´t be aware of Galadriels mindreading? He wants to see her thought, they struggle, but he isn´t able to do but she is.

One time she was able to win in a struggle with him too, when Eorl rode near Lorien.

"When they passed Dol Guldur in Mirkwood - where Sauron dwelled in secret - a darkness emanated from the fortress, and Eorl turned westward to avoid it. But then a white mist came from the woods of Lothlorien that stood across the River from Dol Guldur, and the Riders were hidden and continued safely on their way and, under the protection of the mist, apparently made the journey unwearyingly at an extraordinary rate of speed. "

Apparently Galadriel was able to conquer Saurons shadow, so why not able to read his thoughts?