1. Explain the ideas of Operator Overloading and Object Conversion in OOP C++? 
2. Explain the primary purpose of the following functions?

// Function 1
bool mysteryFunction1(const Point2D& other) {
    return (this->x == other.x && this->y == other.y);
}

// Function 2 
friend Point2D mysteryFunction2(int val, const Point2D& p) {
    return Point2D(p.x + val, p.y + val);
}

// Function 3 
operator double() const {
    return x * x + y * y; 
}

// Function 4 
friend ostream& mysteryFunction4(ostream& os, const Point2D& p) {
    os << "Point(" << p.x << ", " << p.y << ")";
    return os;
}

// Function 5 
int& mysteryFunction5(int index) {
    if (index == 0) {
        return x;
    } else if (index == 1) {
        return y;
    } else {
        throw out_of_range("Invalid index! Use 0 for X, 1 for Y.");
    }
}

3. Integrate these functions into the project and run a demo