Websphere Studio for System I is EOL as of April and the literature on the web page for Rational Developer for Power Systems Software doesn't explicitly mention C compilers.
What is the relationship between RDPS and the "The ILE Compiler set"? Is the latter product still supported?
Is this the right product to build something involving zlib on an iSeries? If not, what should I be talking to IBM about?
(Yes, IBM should be able to answer this but I'm not getting very far)
Don't know about the products of your question. But I do know that the C compiler is still available with V6R1. Notice that this is a full blown compiler with the possibility to do some iSeries specific stuff too.
Please, do understand that these iSeries compilers (e.g. RPG, Cobol) use the ILE model for the compiled objects. This gives you the possibility to link modules from different languages together (something like .Net). But this has nothing to do with the language itself.