As far as removing the adhesive goes as long as you have all the foam off and the adhesive is the only thing left I would not worry about it. Personally I don't use adhesive when I do headliners, I use buttons. Those brass ones that are sold in stationary stores, the kind the split, I put them thru the material, insulation, headliner backer board then put a washer over the backside, bend the legs out then fold them back in so they can't pull back out. I also paint them to either match or contrast with the headliner material. If it is really fancy I'll take some material to a local upholstery shop and have them make a bunch up with the real two piece buttons which have a cap and base and go in a small press, for $2 ea... [expensive], the brass one's come in boxes of 100 for $3, can of rusteolum and 5 min of spraying...done.
As far as the edges go, I fold the material over and around the back of the backer board then double fold it, put the button thru and that will hold it forever.
