Just wondering if the Chromebook uses Linux in some way? If so, would there be a way to run Linux commands (e.g. Ssh) from a command line on it?
Yes, it does use the Linux kernel.
Since the kernel is arguably all that can strictly be called "Linux", the complete OS that we all know and love is more properly called "GNU/Linux". The "GNU" part provides the fundamentals of the userspace (as opposed to kernelspace) and without that, there is no guarantee at all about what software can be used, since software applications exist in userspace, not kernelspace.
Phorce's first link looks pretty decisive tho, so ssh is good. Just don't take the fact that the linux kernel is used to mean it is anything like e.g., Ubuntu, anymore than Android (which also uses the Linux kernel) is.
I believe that the Chromebook does allow SSH.
Also, I think they just pack in ChromeOS (Which I believe is an operating system based upon being online. However, you can install Linux.
Hope this helps, sorry if this does not answer your question.