You can apply the tape to your scalp first, but it will be difficult to get the edge in exactly the same place as the edge of the hairpiece. That doesn't matter too much at the back and sides, because the join will be covered by the hairpiece hair anyway, but at the front it is quite likely that there will be an overlap of bare tape or unattached base. If you want a good result, it would be better to attach the front hairline tape to the hairpiece.
You can lower the density just by pulling hairs out. Soak the hairpiece in warm water for a few minutes, and you will find the hairs can be pulled out fairly easily. Go gently though - it is easy to overdo it.
good luck
Noah
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You can apply the tape to your scalp, but it will be difficult to get a perfect match between the edge of the tape and the edge of the piece. That doesn't matter too much at the back and sides, because the join will be covered by the hairpiece hair anyway, but it could be a problem at the front hairline - you will either get a strip of bare tape showing or a strip of unattached base. So it might be better to put the tape on the unit for the front hairline.
You can pull hairs out of the piece if the density is too high. Soak it in warm water first, and then the knots will pull out more easily. Do it very gradually though - you don't want a patch of bald lace.