Linux install without yum or gcc

The standard for these issues is the Filesystem Hierarchy Standard. It's a rather big document. Basically (and very roughly), the standard paths on Linux are:

• /bin & /sbin are for vital programs for the OS, sbin being for administrators only ;
• /usr/bin & /usr/sbin are for not vital programs, sbin being for administrators only ;
• /var is for living data for programs. It can be cache data, spool data, temporary data (unless it's in /tmp, which is wiped at every reboot), etc. ;
• /usr/local is for locally installed programs. Typically, it hosts programs that follow the standards but were not packaged for the OS, but rather installed manually by the administrator (using for example ./configure && make && make install) as well as administrator scripts ;
• /opt is for programs that are not packaged and don't follow the standards. You'd just put all the libraries there together with the program. It's often a quick & dirty solution, but it can also be used for programs that are made by yourself and for which you wish to have a specific path. You can make your own path (e.g. /opt/yourcompany) within it, and in this case you are encouraged to register it as part of the standard paths ;
• /etc should not contain programs, but rather configurations.

If your programs are specific to the services provided by the service, /srv can also be a good location for them. For example, I prefer to use /srv/www for websites rather than /var/www to make sure the directory will only contain data I added myself, and nothing that comes from software packages.

There are some differences between distributions. For example, RedHat systems use libexec directories when Debian/Ubuntu systems don't.

The FHS is mostly used by Linux distributions (I actually don't know any other OS that really complies to it). Other Unix systems don't follow it. For example, BSD systems tend to use /usr/local for packaged programs, which is not the case for Linux. Solaris has very different standard paths.

I strongly encourage you to read the FHS document I linked above if you wish to know more about this.

Somewhere in /etc/issue the version of CentOS you're dealing with will be shown, and the arch will come from uname -m.

As for yum itself, do not use rpm to reinstall it, but rather use rpm2cpio and cpio to extract the files from the packages and then let yum fix up the rpmdb after the fact. Download the yum and centos-release packages and then:

cd /
rpm2cpio /path/to/yum-....rpm | cpio -id
rpm2cpio /path/to/centos-release-....rpm | cpio -id

Repeat until you have all the packages needed to get yum back in place.