Is there a specific term for false justifications?
I think the examples refer to a variety of possible terms.

In cognitive science, there is much interest in cases where justification is triggered unconsciously.  The general tendency to justify one's decisions - especially the bad ones - is called self-justification:


  Self-justification describes how, when a person encounters cognitive
  dissonance, or a situation in which a person's behavior is
  inconsistent with their beliefs, that person tends to justify the
  behavior and deny any negative feedback associated with the behavior.


When someone makes a decision they know is bad, and uses rational-sounding excuses to obfuscate this, it is called rationalization:


  In psychology and logic, rationalization or rationalisation (also
  known as making excuses) is a defense mechanism in which
  controversial behaviors or feelings are justified and explained in a
  seemingly rational or logical manner to avoid the true explanation,
  and are made consciously tolerable – or even admirable and superior –
  by plausible means.


If scientific-sounding data is added to make a decision seem more objective than it is, then it is called intellectualization:


  Intellectualization is a defense mechanism where reasoning is used to
  block confrontation with an unconscious conflict and its associated
  emotional stress where thinking is used to avoid feeling.


Cherry-picking data to support an argument is an example of confirmation bias:


  Confirmation bias, also called myside bias, is the tendency to search
  for, interpret, prefer, and recall information in a way that confirms
  one's beliefs or hypotheses while giving disproportionately less
  attention to information that contradicts it.


A common view in psychology is that most explanations of decisions made are actually "post-hoc rationalization", or "post-rationalization" (see for example self-perception theory).

Sometimes justification is done consciously / intentionally.  The term you used, cherry picking, is perfectly valid in this case.  Another example is spin.