Practicality of using flat-spiral coil as electromagnet?
1) With this in consideration, is this possible or practical having an
  electromagnet this small and powerful enough to produce the necessary
  field?


Taken from this website, the following picture explains that with 2 turns (as originally specified) and 40 mA current, the magnetic field density at 5 cm from the coil is about 10 nT: -



With 5 turns (as recently specified), the flux density will be 5 times larger at 50 nT.


  2) so it is by definition an electromagnet when a current passes through
  it.


An inductor produces a magnetic field when current passes through its coils.