In your code:
#include <iostream>
using namespace std;
int main()
{
    int* arr = new int;
    arr[0] = 94; // This will work
    arr[1] = 4; // This will cause undefined behaviour
    cout << arr[0] << endl;
}
Int the above code, arr is a pointer to a single int, so you can access that one int using either:
arr[0]
*arr
..but arr1 won't work as there is not enough memory allocated for the array.
To fix this, you must allocate more memory for arr:
int* arr = new int[2];
..and to change the size of arr:
int arr_size = 2;
int* arr = new int[arr_size]; // size of arr = 2
arr[0] = 12;
arr[1] = 13;
int* new_arr = new int[arr_size + 1];
for (int i = 0; i < arr_size; i++)
{
    new_arr[i] = arr[i];
}
delete[] arr;
arr = new_arr;
// size of arr = 3
But all of this gets computationally expensive and time-consuming when arr has a huge number of elements. So I recommend using C++'s std::vector:
Your 2'nd program using std::vector:
#include <iostream>
#include <vector>
struct test
{
    int data;
};
int main()
{
    std::vector<test> vec{ test(4), test(42) };
    std::cout << vec[0].data << std::endl;
}
For more info on std::vector, click here.
Also, consider not using the following line in your code:
using namespace std;
..as it's considered as bad practice. For more info on this, look up to why is "using namespace std" considered as bad practice.