> Q1: What do I need zlib for? Can I safely omit it?
zlib is required for HTTP decompression, and for the internal cache.

> Q3: How can I figure out if zlib comes with Suse 11
> and where it is installed?
You just need to install the zlib-devel package

> libz.so.1.2.5. there. I thought that this shared

You also need the libz.so devel link.