(1) Replace "print `blahblah`" with "blahblah", the backtick (`) is really only useful for storing outputs in variables and using them embedded in other commandlines, if you just want to print the result direct to the screen and nothing else, you don't need them.
eg

Code:

case $x in
"1") ps aux;;
"2") echo "Choose a process to be killed"

(2) You could use killall to do what you want here but I dislike it as it can do horribly wrong on you if you are not careful.

Code:

PIDSIWANTTOKILL=`ps -eo pid,args | awk "/$THINGTOSEARCHFOR/ { print \$1 }"`

Note that if the user puts something silly (like "a" for example) in the THINGIWANTOSEARCHFOR variable, many many many pids can end up in the resultant list.