No you can not install RPMs unless something has changed recently. :)
You have quite a bit of freedom to install things. There are some limitations set on files that normally you would need to change to upgrade or install things but we have found work arounds for many of those. Browse through the forum and you'll get an idea.
WestHost retains the control over most the basics like php, MySQL, Perl, SA and others that are available via the Site Manager. If it is a php or perl script in the Site Apps then you have control over makeing modifications to those. Even though you can't alter the php installation you can change the php.ini same on apache you can edit your httpd.conf. There are others but those are some of them off the top of my head.