required power supply for nichrome heating element?
Is 55.276 volts the amount of volts needed going into my power supply,
  or the amount of volts coming out of my power supply?


That is the voltage you need to put across the nichrome wire, so it will be the output. You're not going to find a 55.276V power supply on the shelf, you're going to have to make your own.


  I have a spare (universal) HP laptop power supply with the following
  specs, is this power supply sufficient for my needs? : Input:
  100-240v, 50-60Hz, 2.0A Output: 18.5v --- 6.5A, 120W


18.5V &lt; 55.276V, so no.


  When I cut the laptop connector off I assume I am going to see at
  least 2, probably three wires. black, white and green (maybe red). Do
  I connection both black/white to one end of the nichrome wire or do I
  connect black to one end and white to the other end?


It won't work like you want, so don't bother, but even if it would work, there is no standard for the color or number of wires in laptop power supplies.


  I may have to get 26 or 30 gauge wire...knowing the above, will my
  power supply still be sufficient with those gauge wires for what I am
  looking to do?


Your power supply isn't sufficicent, but 26 or 30 gauge nichrome wire will have slightly different resistivity than 28 gauge. You'll need to redo your calculations for the gauge you're actually going to use.

It seems like you're pulling a lot of numbers out of thin air. Further, I would be very cautious trusting an online calculator's calculation. The 450F is probably the wire temperature itself. Is that what you really want?