Is it possible for information (like 1 and 0s) to be transmitted faster than light?
This answer has been given already. I'd like to point out, however, that this is utterly self-evident:
It is not possible for signals to be transmitted faster than any signals being transmitted at all.
(In the context of relativistic kinematics "light" plainly means any signal at all having been exchanged between systems constituted of electro-magnetic (or even electro-weak) charges, such as atoms or humans or any sort of observable matter that may be imagined in thought-experiments.)
It is only on this basis that geometric relations are being determined; such as (referring to the example given in the question) whether two people are separated from each other, or whether they meet; or whether two (separated) ends moved rigidly (in relation to each other), or one lagging behind another.
Concretely, the flaw of your example is that two participants who communicate instantaneously are called "meeting" each other; their distance from each other is evaluated as zero.
And otherwise, considering two participants, A and B, who always find being separated from each other, and at rest to each other, they may well find "two ends of a pole" such that A pushing one end was simultaneous to B ejecting the other end (or likewise such that B pushing one end was simultaneous to A ejecting the other end); but only if those occurences are not recognized/considered as exchanges of signals.