A Styrofoam box will help keep the bags insulated from outside air temp changes. It should also be placed in a cardboard box for shipping. If you pack newspaper between the bags, the heat/cold packs can go there if enough room, or on the inside of the lid. Remember, things leak, so seal the bags, Styrofoam box, cardboard box as good as possible.
For anemone removal, you can try any of the following:
Try moving the rock it's on, it may move on its own, point a powerhead at it (gently) and it may move, use an ice cube on the foot and see if it starts to lift, you may be able to peal it off that way. In any of these methods, be very careful, and give the anemone time to recover some before shipping.