Drilling steel without a drill press is a real bummer. You (as in human beings) can't push the bit hard enough to develop the proper thrust force on the drill bit in steel at those sizes. You're going to wear out the bits prematurely unless you take obscenely small steps. Invest in something like a drill doctor for twist drills if you have to use them in steel! I love mine.
A hole saw would be a better tool to use with a hand drill. Thrust loads for proper cutting are lower, less material is chipped (so you use less energy to make the hole), and good hole cutters will take a lot more abuse than a generic twist bit. See:
https://www.mcmaster.com/4093a41
For cutting oil, just use whatever you have that isn't toxic. In my shop we use Boeshield and WD40 as cutting fluids. Occasionally motor oil. Often we'll use a water-based coolant on our mill.