So long as the app has an API interface, yes it can..
Can a Java app on a UNIX server interact (two way) with an SPSS app on a mainframe?
Yes infact we do some of that at my shop, our Java guys are pretty sharp. There is a company called openconnedt that sells such products as well.
Can a php app on a UNIX server call any procedural code (RPG, COBOL, etc.) on a second, remote server (other than the one on which the php app is installed) in which Java is not enabled?
Yes so long as the other serve is listening for it, mind you directly calling is an aweful idea and leads to security mess later down the road..