i believe the stuff i use to use at the shop was called k kwik i think it was from home depot, ill do some searching soon and pm you. since you have the stock padding on back you can probably get away with wrapping it around contact adhesive and a staple or two on the back side.
as for fabric, some stuff is foamyand i wouldnt recommend that, you could use basic vinyl or polyester,cotton or whatever it is that you get at places such as joanne fabrics, if your familiar with that. otherwise search for fabric places around you and ask if they have any automotive interior upholstery you could use on door panels thats plain blakc, or whatever your looking for. or get it online, ossibilites are endless.
cant remember or find the adhesive we use. weve used 3M in the past in cans thats a good temporary hold but weve had some picky times with it. also DAP makes good stuff but some of it isnt for use on foam so be careful of that. ill keep searching, maybe al can lead you in the right direction on this one because i havent the slightest rememberanc eof the brands name.