Transformer behavior for complete dummies
Considering an ideal transformer (without losses) and an open circuit
  on the secondary, could the current on the primary be calculated as:
  =/(2)


That is entirely correct and that current is called the primary magnetization current.


  I am under the (possibly wrong) impression that since there is no load
  on the secondary, the power dissipated on the primary should be 0, and
  as such no current would flow through it.


Correct, for an ideal transformer this is entirely true.


  say I removed the secondary from some transformer and was left with
  just a piece of copper wire wound about an iron core, would the
  current flowing through this inductor be calculated the same way as if
  there was a secondary wound on the core?


Yes, but, if the unloaded secondary was left in place you’d still get the same primary magnetization inductance.