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While mapping out the position, distance and movement of galaxies and quasars at the limits of the observable universe, have astronomers ever observed the motion of these object due to gravitational sources that may reside outside the limits of the observable universe?

If so, would this break the principle of information travelling faster than the speed of light?

If not, are these objects in fact the furthest objects there are?

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No, it would not violate the principle of special relativity, which proscribes information traveling faster than the speed of light. Let's call the farthest object we can see X. Let's call X's neighbor on the far side from us Y. The only way for us to get information about Y is for information to travel to X (at or below the speed of light), which would then influence X's behavior. Then, information about X's behavior would have to travel to us (at or below the speed of light). So, nowhere is information traveling faster than light. The only information we can get from X about Y is already "out of date"* enough that special relativity isn't violated.

*The technical term relativists use is "retarded," but be careful how you use it in everyday conversation.

EDIT: We can make a distinction between the theoretically observable Universe according to relativistic considerations, which is what I was talking about above, and the Universe observable with present technology and practical limitations. Getting sneaky like inferring about Y from X actually does increase the latter meaning of observable Universe.

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If it's a real phenomenon the Dark Flow is the motion of the entire observable universe relative to the CMB due to attraction to something that was inflated beyond the horizon. ~~The validity of the theory is currently disputed and probably not resolvable until better data is made available from the Plank satellite's CMB measurements.~~ Even after the Plank data has become available, different research teams continue to dispute if it is a real phenomenon. The Plank team itself claims to have invalidated it, but the original proposer of the theory claims to still see it in the Plank data.

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