I'm not sure about the first three but I would guess that Eleanor or someone else told him something then he called for Galadriel to come

I dont think it would be spies though I know someone answerred this awhile back but Saruman always had a distrust for him. Galadriel and Elrond originally wantedd Gandalf to be the head, but Saruman became the head. I'm not sure if this part is right but he always thought he was going to overthrow him because he wanted power but it was him that was greedy and wanted power. At the end of The Return of the.King I think he said something either like "you wanted this" or "you've always been scheming to do this." When Galadriel came. I don't think Saruman was evil until he looked into the Palantir even though he always wanted power so he probably didn't know by the time Bilbo's adventure began.

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You can (and surely should) disable that “feature”, you know.

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…all eyes looked upon the ring; for he held it now aloft, and the green jewels gleamed there that the Noldor had devised in Valinor. For this ring was like to twin serpents, whose eyes were emeralds, and their heads met beneath a crown of golden flowers, that the one upheld and the other devoured; that was the badge of Finarfin and his house.

The Silmarillion, pp 150-151

while Felagund laughs beneath the trees

in Valinor and comes no more
to this grey world of tears and war.

The Lays of Beleriand, p 311

Here now for seven days they tarried, for the time was at hand for another parting which they were loth to make. Soon Celeborn and Galadriel and their folk would turn eastward, and so pass by the Redhorn Gate and down the Dimrill Stair to the Silverlode and to their own country. They had journeyed thus far by the west-ways, for they had much to speak of with Elrond and with Gandalf, and here they lingered still in converse with their friends. Often long after the hobbits were wrapped in sleep they would sit together under the stars, recalling the ages that were gone and all their joys and labours in the world, or holding council, concerning the days to come. If any wanderer had chanced to pass, little would he have seen or heard, and it would have seemed to him only that he saw grey figures, carved in stone, memorials of forgotten things now lost in unpeopled lands. For they did not move or speak with mouth, looking from mind to mind; and only their shining eyes stirred and kindled as their thoughts went to and fro. (my emphasis)
- Many Partings, ROTK