Perplexing Chimera + Hypnotic Siren. Do I control all of my opponent's spells?
No, this does not work. Exchanging control using Chimera's ability sets up a continuous effect; the same as the one created by Hypnotic Siren (or Mind Control, etc). When there are multiple effects that are applied in the same layer, they are all applied in timestamp order. This means that because the Chimera's ability resolved after the Siren's ability, your opponent will get the Chimera back.


  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.
  


Discussion on this interaction with Mind Control here.