Linux – make a linux “from scratch” using package manager

In general, just using yum is not sufficient for package compatibility. The rpm package format is relatively flexible, in the sense that it doesn't impose much by way of policy. The R package you want to use could be packaged such that they're distribution agnostic and just need to be unpacked via yum. However, it is more likely that they follow a whole host of assumptions about the distribution beyond yum itself — what libraries are available, what they're named, where they put their files (and what rpm packages those things come from).

In that case, you'll be best off with Red Hat Enterprise Linux itself, or with CentOS or Scientific Linux (both of which are built from the source packages provided by Red Hat). You may also be able to use Fedora, which is a community-built distribution in the same "family" (and generally much more desktop focused and bleeding edge).

AFAIK the only way to be completely sure of security would be to write a compiler in assembly language (or modifying the disk directly yourself). Only then can you ensure that your compiler isn't inserting a backdoor - this works because you're actually eliminating the compiler completely.

From there, you may use your from-scratch compiler to bootstrap e.g. the GNU toolchain. Then you could use your custom toolchain to compile a Linux From Scratch system.

Note that to make things easier on yourself, you could have a second intermediary compiler, written in C (or whatever other language). So you would write compiler A in assembly, then rewrite that compiler in C/C++/Python/Brainfuck/whatever to get compiler B, which you would compile using compiler A. Then you would use compiler B to compile gcc and friends.