How do I pass on script arguments that contain quotes/spaces?

Use "$@" with quotes:

prog="$1""$@"ecode="$?"echo "$prog exited with $ecode"

This will pass each argument exactly as it was received. If you don't include the quotes, each element will be split according to $IFS:

• "$@" is like "$1" "$2" "$3" ..., passing each element as a separate argument.
• "$*" is like "$1 $2 $3 ...", passing all elements concatenated as a single argument
• $* and $@ is like $1 $2 $3 ..., breaking up each element on whitespace, expanding all globs, and passing each resulting word as a separate element ($IFS).

The same is true for arrays, such as "${array[@]}" and "${array[*]}"

Put double-quotes around your variable substitutions to keep them from being parsed (note that this applies to all variables: $@, $1, and $PROG). Also: don't put a $ before a variable name when assigning to it; use # for comments; and, on the last line, the single-quotes will prevent variables from being substituted at all.

PROG="$1"shift# Run program below"$PROG" "$@"ECODE=$? # note: this will always be a number, so it doesn't have to be protected with double-quotesecho -e "Subject: $(hostname): $PROG finished\r\nTo: <$USER>\r\n\r\nExited with $ECODE\r\n' | sendmail "$USER"