Would loading a linux live CD to RAM improve battery life? (knoppix toram or SLAX Copy to RAM option) Compared to running it from the CD.
Would booting a Live CD off of a USB increase battery life more than using a CD?
Yes as this would avoid constantly reading the CD/USB drive. Furthermore, you could save more power by shutting the hard drive off if you can. Depending on if you're at idle or under load, and what the hard drive is doing, it generally consumes 10-20% of the laptop's total power consumption (although this is highly dependent on the particular laptop, hard drive, usage patterns).
Yes but negligible. An optical drive might use more power than a USB stick would while reading, but you're not technically reading for very long in most cases, unless you happen to reboot insanely frequently; also a flash drive can be used for persistent storage, giving it another advantage.
When you are running from a Live CD, the operating system will constantly need to read files from the disc (usually when you start an application), so the optical drive will spin in order to read the data. Of course, the process of reading data from the disc uses electricity. The motor needs to be powered in order to spin the disc for reading.
If you use a Live USB (flash drive) instead, it will most likely use less electricity. The majority of USB flash drives use NAND flash, which doesn't consume much power. An optical drive, however, needs to power a stepping motor to spin the disc. Most likely that powering the stepping motor will consume more power than reading from NAND flash.
If you load the Live CD to RAM, the operating system doesn't need to read from the disc again after the data is loaded to RAM at first, so if you run the Live system for a long time without restarting, the optical drive should not consume much power since it will most likely not spin at all. However if you restart frequently, the disc will need to be re-copied to RAM and thus consume more power.