As with every other thing about fitting the scales to be flush, go slowly and take off a little at a time until you get the right fit.
On every step leave extra material for yourself in case you make a mistake until you are 100% sure you don't want to profile any further. Use your power tools until you have a few mm left, then do the rest by hand. Trust me, an amateur slip on a belt sander will bit deep and leave you having to re-sand the whole thing to make it smooth.
case in point: my own Birch scale project I've been on that last few days.
http://www.bladeforums.com/forums/showthread.php/1209979-Making-wood-scales-for-Esee4
I don't have a drill press so I had to do the holes by hand, countersinking was a huge pain without the proper tools but I was able to fit them properly by going little by little. It's not symmetrical or clean but they fit just fine. It helped that I wanted my scales to be very rounded; I was able to get away with rounding out my countersinks to be less noticeable.
Many people will glue their scales on in addition to pins or screws. Most epoxys would be able to hold strong enough, the pins just help the scales from shearing off if dropped or something.
As for measuring how far the countersink goes try putting one side of the original scales, then line up your stock piece on the other side to get and idea of how deep that screw will need to sit to reach properly.
Other than that most of those screws are common threads, so you should be able to find longer replacements at your hardware store.