Tom, if you go ahead with this effort, you will need PROPER lubricant. I strongly suggest, for swaging less than 1000 bullets a year, using one of those one ounce tubes of anhydrous lanolin you can buy for $2 at most drug stores. If you apply a very small dab to your thumb and forefinger, you can roll the bullet between them to apply just a VERY thin film of lub immediately before waging. Regular "case" or "reloading" lub may not work well for this job. 1 oz of Lanolin should last at least thru 1000 bullets. The key word is THIN. And, it washes off in plain warm water.
The core does seperate from the jacket (unless it's a bonded core bullet you are swaging) during reduction depending on many factors. Usually, this seperation is absolutely inconsequential if the reduction is below .005". If the jacket is of some really hard brass, or steel, you may have problems at even .004". I've reduced many off-the-shelf bullets of several calibers, and as long as I've kept under .006" in one pass, I've never had a problem. Too, while I've reduced Jackets (by themselves) in several stages, up to .037", I've never attempted to reduce a bullet further than one pass thru a die.