Do the work early in the morning.
The "glue" tabs will snap open easier.
Be careful not to bend the shingles too much though.
They will be stiff.
^^^^This^^^^
In the early morning, when the shingles are cool, slide a large blade putty knife under the top shingle to break the seal. Do not bend the shingle back yet though. You will also have a nail on your starter strip, but it may be up far enough out of the way. Two ways around that......either get a flat bar and pop the nail out, or you may have to notch the drip edge.
Once you have the shingles loose from prying them apart, go have a few cups of coffee until the sun hits the shingles and they become more pliable. You'll have to carefully raise it up enough to get the nail and hammer in there.
Depending on where you are at, if anywhere around my area, we aren't going to have too many hot days left, so get a tube off asphalt sealer, or soe sort of a good caulking, and fasten your shingles back down to the starter after you get things nailed.
And to answer your first question......You DO NOT want to nail the drip edge in the front. For one, that's just halfassing things and would look tacky. Even though it will take a little longer, do it the right way.
NOW......if the drip edge does not hang down over your gutters, you may want to pick up some coil stock, and put it into the gutter up to the bottom of the shingles on the fascia, then put your drip edge on. Water has a tendency to siphon back on the small flared lip of drip edge, and that is when you get water running behind your gutters. A piece of flashing will eliminate that. Byt all rights, when a gutter is hung correctly, it should be up under your drip edge in the first place.