Is it possible to replace battery in an old iPad? I have an old iPad 2.  The battery goes dead when it is unused for only one day. Should I change the battery and if yes, how should I do it?
Yes it's possible, but it's incredible hard for almost any average or advanced user, so I highly recommend against it, sorry.

Here is a nice step by step guide from the folks of iFixit, if you are (really) adventurous enough...

Best luck!