I need to see currently installed updates and security patches on Linux Gentoo. How I can do this?
The Gentoo Linux Security Team releases Security Advisories (GLSAs) which can be checked with glsa-check if your system is affected by the given security advisories. You just have to sync your portage tree (emerge --sync) and then run glsa-check -l and it will tell you which known security holes you have and how to solve them.
And very important is Maintenance. This article shows how to keep your system up to date and clean.