I think you really need to work on commands one at a time
. Be sure you understand how each command works before trying to write a script.
First, you don't need to modify a variable "so I can use it with SED". Just make the SED statement do what you want directly. In your example, you want to remove something from the PATH variable which appears in /etc/profile. Let's start with a simple example. To remove all of the entries "/root/bin", do this:
sed -i '/^PATH/s%/root/bin:%%g' /etc/profile
The -i flag tells sed to edit the file "in place". Note that you don't need to "cat" the file and then pass it to sed. Note that I used "%" as the delimiter, since "/" appears in the actual text to be changed. The logic of this sed construct is:
find all lines beginning with "PATH", and replace all occurrences of /root/bin with nothing. Note also the added ":"
Now, suppose you want to use the content of a variable to determine what to remove:
sed -i "/^PATH/s%$var:%%g" /etc/profile
Note that I changed the single quote to a double. This is necessary to allow "$var" to be expanded before sed executes.
In addition to the text I suggested, go here for a very good SED tutorial: http://www.grymoire.com/Unix/Sed.html