Since you have the battery on hand, I'm going to assume you noticed the contacts on the battery require soldering. If you were unaware of that, STOP, and find someone who has experience soldering or you may render the iPod useless.
As far as adhesive for the copper tape, are you referring to the copper tape under the battery? If so I have done many iPod touch 4th gen batteries and have managed to remove the old battery without taking out that copper tape, so it is possible to do it that way you may just have to pry between the two. If you do remove it and it is in good shape there shouldn't be an issue setting it back in the shell as it is extremely sticky and not likely to let the battery move about in the shell when the job is done.
When your reassembling the two halves back together, you have two options, if the tape on the rim looks in good shape(free of trash ect...) and mostly intact(covering most of the lip) you may be able to get away with reusing what you have for a while. If you tear up the adhesive while working on the device i recommend replacing it, you can get OEM ipod shell shaped adhesive or you can buy 3M high strength bonding tape, basically really strong and THIN double sided tape and tailor the shape of it to your needs. Also this tape can be used to reapply adhesive to the copper tape I talked about earlier.
Good luck on your repair, I hope this helps, and I hope everything goes smoothly. :)