How do Mistform Dreamer and Conspiracy interact?
1) No; in fact, the creature subtype 'Wall' has long since lost any rules weight, and there's no reason that Walls can't attack other than that they have (either through print or via errata) the 'defender' ability: if a Wall were printed without defender, then it would be able to attack just like any other creature.  This is confirmed in the rulings you can find on the Gatherer page for Conspiracy:


  8/1/2005  If you choose Wall, then your creatures can still attack because
  creature types don't confer abilities such as defender (any more than,
  say, choosing creature type Bird would confer flying).


2) This becomes a bit more complicated.  The key notion is the concept of timestamping; you can find the specific details in section 613.6 of the comprehensive rules, but the key pieces are these:


  613.6. Within a layer or sublayer, determining which order effects are applied in is usually done using a timestamp system. An effect with an
  earlier timestamp is applied before an effect with a later timestamp.
  
  613.6a A continuous effect generated by a static ability has the same timestamp as the object the static ability is on, or the timestamp of
  the effect that created the ability, whichever is later.
  
  613.6b A continuous effect generated by the resolution of a spell or ability receives a timestamp at the time it’s created.


Because the effect generated by the resolution of Mistform Dreamer's ability to set its creature type is 'newer' than the effect generated by Conspiracy, the subtype change from Conspiracy is applied first, then the subtype change from the Dreamer's own ability, leaving the Mistform Dreamer as whatever subtype you set it with its own ability.  But note that this effect will wear off at EOT when the ability is cleaned up, and whenever you haven't activated Mistform Dreamer's ability in a turn, it will be whatever creature type Conspiracy is set to.