Fatorangekat,
While it's possible to use a drill to open up the hole on a prop in a hand drill is possible, it's not recommend. The best way to open up the hole in the prop is to use a reamer to widen the hole. This is because it will keep the hole in the center of the prop and not throw the prop out of balance. If you must use a drill to open up the hole then you should use a drill press to do it with. this way you can secure the prop so that it doesn't pull off center when you start drilling out the hole.

For your second question. No, "snug" is not tight enough. If you just snug it down it's a pretty sure bet that the prop is going to get thrown when you try to start the engine. When you put the prop on you need to get it as tight as possible. I recommend using a box end wrench so that they wrench doesn't slip and round the nut. Then get a good leather glove for one hand to hold the prop with so that it doesn't cut you hand, or use a good rag and wrap around the prop. Then to tighten the nut down use the prop to help you tighten it. Grab the prop and the wrench with the hand in the glove (or rag) and pull them together to tighten the nut. This leverage will get the nut tight enough to keep the prop from being thrown. Don't worry about stripping out the nut or shaft as they are both made of steel and aren't going to strip. This is how I secure my props and I haven't thrown a prop from any plane in over 8 years.

Hope this helps

Ken