@pschwede in the system im writing wrong person isnt related to collisions, it makes no logical sense as a question.
As for sending the same money twice, transactions are ordered so whichever one succeeds first goes through if there is limited funds to cover both. If a person owns enough fuds to cover both then both parties would be paid.
Remember this is a ground up redesign of the cryptocurrency paradigm that is so different many of these questions are non-questions.