I am very new and trying to figure out if it is possible to record from a regular cassette player to a cd-rw without having to go through the computer?
The short answer is no, unless your cd-recorder is some flavour of Alesis Masterlink or something similar.
The other to point out is that you don't want to be recording audio cds onto CD-RWs - most audio cd players cannot read CD-RW discs. However, most (not all) can read CD-R discs.