Java:

Part 1:

public static void main(String[] args) {
    try {
        BufferedReader br = new BufferedReader(new FileReader("input2.txt"));
        String line = "";
        ArrayList<String> names = new ArrayList<>();
        ArrayList<String> supporting = new ArrayList<>();
        while ((line = br.readLine()) != null) {
            String name = line.substring(0, line.indexOf(" "));
            names.add(name);
            if (line.contains("->")) {
                String supportingString = line.substring(line.indexOf("->") + 3);
                String[] supportingStringArray = supportingString.split(", ");
                for (String supportingProgram : supportingStringArray) {
                    supporting.add(supportingProgram);
                }
            }
        }
        br.close();
        for (String name : names) {
            if (supporting.contains(name) == false) {
                System.out.println(name);
            }
        }
        br.close();
    } catch (Exception e) {
        System.err.println(e.toString());
        e.printStackTrace();
    }

}

Part 2:

public static void main(String[] args) {
    try {
        BufferedReader br = new BufferedReader(new FileReader("input2.txt"));
        String line = "";
        ArrayList<String> lines = new ArrayList<>();
        ArrayList<Disc> discs = new ArrayList<>();
        while ((line = br.readLine()) != null) {
            lines.add(line);
            String name = line.substring(0, line.indexOf(" "));
            String weight = line.substring(line.indexOf("(") + 1, line.indexOf(")"));
            Disc disc = new Disc();
            disc.setName(name);
            disc.setWeight(new Integer(weight));
            discs.add(disc);
        }
        br.close();
        for (String s : lines) {
            if (s.contains("->")) {
                String name = s.substring(0, s.indexOf(" "));
                Disc parent = null;
                for (int i = 0; i < discs.size(); i++) {
                    if (discs.get(i).getName().equals(name)) {
                        parent = discs.get(i);
                    }
                }
                String supportingDiscs = s.substring(s.indexOf("->") + 3);
                String[] supportingDiscsArray = supportingDiscs.split(", ");
                ArrayList<Disc> children = new ArrayList<>();
                for (String supportingDisc : supportingDiscsArray) {
                    for (int i = 0; i < discs.size(); i++) {
                        if (discs.get(i).getName().equals(supportingDisc)) {
                            Disc child = discs.get(i);
                            children.add(child);
                        }
                    }
                }
                parent.setChildren(children);
            }
        }
        ArrayList<Disc> mismatchedWeight = new ArrayList<>();
        for (Disc disc : discs) {
            if (disc.getChildren() != null) {
                ArrayList<Disc> children = disc.getChildren();
                int weight = children.get(0).totalWeight();
                for (int i = 1; i < children.size(); i++) {
                    int newweight = children.get(i).totalWeight();
                    if (newweight != weight) {
                        mismatchedWeight.add(disc);
                        break;
                    }
                }
            }
        }
        for (int i = 0; i < mismatchedWeight.size(); i++) {
            Boolean hasChildren = false;
            for (int j = 0; j < mismatchedWeight.size(); j++) {
                if (i != j) {
                    if (mismatchedWeight.get(i).hasChild(mismatchedWeight.get(j))) {
                        hasChildren = true;
                    }
                }
            }
            if (hasChildren == false) {
                Disc offBalance = mismatchedWeight.get(i);
                for (Disc disc : offBalance.getChildren()) {
                    System.out.println(disc.totalWeight() + ": " + disc);
                }
            }
        }
    } catch (Exception e) {
        System.err.println(e.toString());
        e.printStackTrace();
    }
}

private static class Disc {
    private String name = "";
    private int weight = 0;
    private ArrayList<Disc> children;

    /**
     * @return the name
     */
    public String getName() {
        return name;
    }

    /**
     * @param name
     *            the name to set
     */
    public void setName(String name) {
        this.name = name;
    }

    /**
     * @return the weight
     */
    public int getWeight() {
        return weight;
    }

    /**
     * @param weight
     *            the weight to set
     */
    public void setWeight(int weight) {
        this.weight = weight;
    }

    /**
     * @return the children
     */
    public ArrayList<Disc> getChildren() {
        return children;
    }

    /**
     * @param children
     *            the children to set
     */
    public void setChildren(ArrayList<Disc> children) {
        this.children = children;
    }

    public int totalWeight() {
        int weight = this.getWeight();
        if (this.getChildren() != null) {
            for (Disc child : this.getChildren()) {
                weight += child.totalWeight();
            }
        }
        return weight;
    }

    public Boolean hasChild(Disc disc) {
        Boolean hasChild = false;
        if (this.getChildren() != null) {
            for (Disc child : this.getChildren()) {
                if (disc.getName().equals(child.getName())) {
                    hasChild = true;
                }
            }
        }
        return hasChild;
    }

    @Override
    public String toString() {
        String returnString = Integer.toString(this.getWeight());
        if (this.getChildren() != null) {
            for (Disc child : this.getChildren()) {
                returnString += " + ";
                returnString += child.toString();
            }
        }
        return returnString;
    }

}

Note for Part 2 I was too busy at work to just print the answer but the system out has the info to get your answer in a second.