Can we put hardwood over concrete floors that have been painted and sealed? My concern is that the glue will stick to the current finish and eventually start to separate. So we will have wood that is shifting. Any experience with this issue will be appreciated.

Paint needs to be removed for a successful glue bond. There are paint/adhesive removal type machines designed just for this purpose.

http://www.youtube.com/watch?v=mxPjEGraCjk

Even if your home is built on a concrete slab, you can still enjoy the beauty of hardwood floors. Concrete should be dry and the right subfloor and vapor retarders. Hardwood floor can be installed on slabs that are either on grade or above grade. However, moisture can cause problem for hardwood floor below ground level, so engineered wood floors are the best choice.

Nail down plywood and nail 3/4 solid to that. That's the only product I trust. I never trust glue or laminate/engineered floors. I trust what I see still alive and well in 150 year old homes. Solid wood.