Ansi C linked list

#include <stdio.h>
#include <stdlib.h>

typedef struct node
{
    int value;
    struct node* next;
} node_t;

node_t* new_node(int value)
{
    node_t* new_node = (node_t*)malloc(sizeof(node_t*));
    new_node->value = value;
    new_node->next = NULL;

    return new_node;
}

void print_list(node_t* head) {
    while(head != NULL) {
        printf("%d -> ", head->value);
        head = head->next;
    }

    printf("NULL");
}

node_t* attach_node(node_t* head, int value) {
    node_t* new_head = new_node(value);
    new_head->next = head;

    return new_head;
}

node_t* append_node(node_t* head, int value) {
    // Head does not change
    node_t* head_it = head;

    if(head_it == NULL) {
        return new_node(value);
    }

    while(head_it->next != NULL) {
        head_it = head_it->next;
    }

    // head->null here
    head_it->next = new_node(value);

    // Return the original head
    return head;
}

node_t* insert_at(node_t* head, size_t index, int value) {
    // Head does not change
    node_t* head_it = head;

    if(head_it == NULL && index != 0) {
        return NULL;
    }

    for(size_t i = 0; i < index && head_it->next != NULL; i++) {
        head_it = head->next;
    }

    // i == index or head->next == NULL
    if(head_it->next == NULL) {
        // End of the list reached, adding element at the end
        head_it->next = new_node(value);
        return head;
    }

    // i == index
    node_t* link = head_it->next;
    head_it->next = new_node(value);
    head_it->next->next = link;

    return head;
}

int main(void)
{
    node_t* head = new_node(10);
    head->next = new_node(13);
    head->next->next = new_node(41);

    print_list(head);
    printf("\n");

    head = append_node(head, 99);

    print_list(head);
    printf("\n");

    head = attach_node(head, 12);

    print_list(head);
    printf("\n");

    head = insert_at(head, 2, 66);

    print_list(head);
    printf("\n");

    return 0;
}