If I were to run a Linux LiveCD regardless of the underlying operating system I am running, am I subject to the same problems I can run into when using the installed operating system? What are the limitations of a LiveCD when security is paramount?
No. Firstly viruses are often platform specific. Secondly, the livecd is running off ram, and the base system is read-only, with any changes either being ignored, or on a overlay file system.
The installed OS affects the livecd in no way at all.
If security is the main consideration, livecds are perfect - you can verify that they're not tampered with, and if you turn off the system all data are lost.
No. The liveCD itself is safe from getting infected by viruses. No virus could get written to it.
lets say the internal hard disk has a virus. You could access the internal hard drive and its infected data. Depending on the virus and how it operates, you could activate the virus. It could affect how your LiveCD OS operates in that particular session, as well is infecting more data on your internal storage and the internet.