1) There are several techniques to tell the difference between encrypted data and random noise(like a pet walking on a keyboard), some of them are surprisingly simple, like simply matching up the ratios of repeated patterns to an expected curve.
2) A message sent back in time providing instruction on how to avert a catastrophe does not necessarily create a paradox, since the people who take action to avert said catastrophe will likely be aware that they still need to send the same message that they received back to the past, i.e. the original sender may cease to exist, but that doesn't prevent a new sender carrying out the originals's task. This is a fairly simple 1 cycle loop with a valid entry and exit point, so no paradox is necessarily created.
3) Depending on exactly what flavour of time travel is being used (parallel worlds, diverging/branch timelines, single collapsing timeline, etc) The original communication has many potential origins and the potential effect it has on future events could even be completely meaningless to either the ones who sent it, the ones who received it, or even both parties. i.e. the recipients are not subject to the same disaster that the sender experienced. The recipients are subject to said disaster but the actions after being warned actually cause said disaster, or a different even worse one (perhaps the sender even had malicious intentions?). The sender successfully saves the recipient but are themselves not saved as their own disastrous timeline continues on, etc.