1. How to get list of dependencies of non-installed RPM package?

apt-cache show <package> shows also it's dependencies.

yum info <package> does not show dependencies, but it obviously                know them.

How to ask yum for dependencies of specified package?

yum doesn't have that capability. Use repoquery instead.

repoquery --requires <package>

2. How do I need to set up my local repository so that I only need to run yum update from the client without having to clean my yum cache? You can run "yum clean expire-cache" which is much more efficient way to tell yum to check the repos. ... the other thing to do would be to change the metadata_expire value for the local repo. (see man yum.conf).

Try adding following line in /etc/yum.conf on Yum clients:

metadata_expire=1m

Following command shows you more info:

man yum.conf

FYI. CentOS 5 has the parameter commented out. CentOS 6.2 has 90m for the value.