You can use a battery drill or a corded drill. A 3/8 drill could work the best, a 1/4 is just a bit on the light side, but it will work.
The knob hole would work, but the hole for the striker only sets at 1 3/8" or 1 1/2"
The kit comes with a threaded center pilot bit, which tends to tighten when drilling and can become difficult to separate. It does not come with the nicer arbor with locking pins to prevent the arbor from over tightening on the hole saw. I’ll try to attach a photo.
Yes, the hole saws are Bi-Metal and will work on metal skinned doors. Just let the saw do the cutting at a medium-low speed to get through the metal into the wood. I would mark both sides of the door, cut on one side of the door until the pilot bit just come through and than cut from the other side. It does not push out the metal skin as it gets heated, it leaves the burrs to the inside and you'll be able to pull out the cut-out plug from the saw easy.
Hole saws do not work very will with existing holes. They have a pilot bit for new work and will be very difficult to control in an existing hole.
Yes it comes with a pilot bit.
yes, kit includes 2 1/8 bit