Yes, Illumina have their own proprietary analysis pipeline:

1. GOAT for Image Analysis (no alternatives)
2. Bustard for Base Calling (maybe there are alternatives, but you should use Bustard)
3. GERALD for alignment, visualization, and filtering. Can export data as fastq.
4. ELAND maps reads to the human genome with 0, 1, or 2 mismatches in the first 32 base-pairs
5. PhageAlign a very slow but exhaustive aligner
6. And finally CASAVA (Consensus Assessment of Sequence and Variation) does the SNP calling and Indel Detection. CASAVA takes Illumia specific format as input. CASAVA is also used to do the sample de-multiplexing.

After we get the fastq files we don't normally use Illumina's software.

Our data published in that paper have been analyzed by a company named Integragen who used CASAVA.

People use the provided pipelines to make fastq's but I don't think people use CASAVA. Just looking at the seqanswers board, no one writes in asking questions about CASAVA, or answers questions with "This is how you get CASAVA to do what you want". I doubt this board looks much different. I looked at it a year or so ago, and there was bad regex in one of the perl parts of it, and it wouldn't deal with multi-fastas, even though ELAND would, and it wasn't obvious how to get a microbial genome on to it. I spent a little while trying, and I gave up.

With the new version, it might be a hair more useful, but if you need help, you are probably better off asking online with the academic tools that lots of people use and understand (and where sometimes the authors are good enough to chime in on) than asking Illumina to help you figure out CASAVA.