Is it good programming practice in C to use first array element as array length?

Well, it's bad in the sense that you have an array where the elements does not mean the same thing. Storing metadata with the data is not a good thing. Just to extrapolate your idea a little bit. We could use the first element to denote the element size and then the second for the length. Try writing a function utilizing both ;)

It's also worth noting that with this method, you will have problems if the array is bigger than the maximum value an element can hold, which for char arrays is a very significant limitation. Sure, you can solve it by using the two first elements. And you can also use casts if you have floating point arrays. But I can guarantee you that you will run into hard traced bugs due to this. Among other things, endianness could cause a lot of issues.

And it would certainly confuse virtually every seasoned C programmer. This is not really a logical argument against the idea as such, but rather a pragmatic one. Even if this was a good idea (which it is not) you would have to have a long conversation with EVERY programmer who will have anything to do with your code.

A reasonable way of achieving the same thing is using a struct.

struct container {
    int *arr;
    size_t size;
};

int arr[10];

struct container c = { .arr = arr, .size = sizeof arr/sizeof *arr };

But in any situation where I would use something like above, I would probably NOT use arrays. I would use dynamic allocation instead:

const size_t size = 10;
int *arr = malloc(sizeof *arr * size);
if(!arr) { /* Error handling */ }

struct container c = { .arr = arr, .size = size };

However, do be aware that if you init it this way with a pointer instead of an array, you're in for "interesting" results.

You can also use flexible arrays, as Andreas wrote in his answer

In C you can use flexible array members. That is you can write

struct intarray {
   size_t count;
   int data[];  // flexible array member needs to be last
};

You allocate with

size_t count = 100;
struct intarray *arr = malloc( sizeof(struct intarray) + sizeof(int)*count );
arr->count = count;

That can be done for all types of data.

It makes the use of C-arrays a bit safer (not as safe as the C++ containers, but safer than plain C arrays).

Unforntunately, C++ does not support this idiom in the standard. Many C++ compilers provide it as extension though, but it is not guarantueed.

On the other hand this C FLA idiom may be more explicit and perhaps more efficient than C++ containers as it does not use an extra indirection and/or need two allocations (think of new vector<int>).

If you stick to C, I think this is a very explicit and readable way of handling variable length arrays with an integrated size.

The only drawback is that the C++ guys do not like it and prefer C++ containers.

It is not bad (I mean it will not invoke undefined behavior or cause other portability issues) when the elements of array are integers, but instead of writing magic number 9 directly you should have it calculate the length of array to avoid typo.

#include <stdio.h>

int main(void) {
    int arr[9]={sizeof(arr)/sizeof(*arr),0,1,2,3,4,5,6,7};
    
    for (int i=1; i<arr[0]; i++) {
        printf("%d ", arr[i]);
    }
    return 0;
}

Only a few datatypes are suitable for that kind of hack. Therefore, I would advise against it, as this will lead to inconsistent implementation styles across different types of arrays.

A similar approach is used very often with character buffers where in the beginning of the buffer there is stored its actual length.

Dynamic memory allocation in C also uses this approach that is the allocated memory is prefixed with an integer that keeps the size of the allocated memory.

However in general with arrays this approach is not suitable. For example a character array can be much larger than the maximum positive value (127) that can be stored in an object of the type char. Moreover it is difficult to pass a sub-array of such an array to a function. Most of functions that designed to deal with arrays will not work in such a case.

A general approach to declare a function that deals with an array is to declare two parameters. The first one has a pointer type that specifies the initial element of an array or sub-array and the second one specifies the number of elements in the array or sub-array.

Also C allows to declare functions that accepts variable length arrays when their sizes can be specified at run-time.

It is suitable in rather limited circumstances. There are better solutions to the problem it solves.

One problem with it is that if it is not universally applied, then you would have a mix of arrays that used the convention and those that didn't - you have no way of telling if an array uses the convention or not. For arrays used to carry strings for example you have to continually pass &arr[1] in calls to the standard string library, or define a new string library that uses "Pascal strings" rather then "ASCIZ string" conventions (such a library would be more efficient as it happens),

In the case of a true array rather then simply a pointer to memory, sizeof(arr) / sizeof(*arr) will yield the number of elements without having to store it in the array in any case.

It only really works for integer type arrays and for char arrays would limit the length to rather short. It is not practical for arrays of other object types or data structures.

A better solution would be to use a structure:

typedef struct
{
    size_t length ;
    int* data ;
} intarray_t ;

Then:

int data[9] ;
intarray_t array{ sizeof(data) / sizeof(*data), data } ;

Now you have an array object that can be passed to functions and retain the size information and the data member can be accesses directly for use in third-party or standard library interfaces that do not accept the intarray_t. Moreover the type of the data member can be anything.

Obviously NO is the answer. All programming languages has predefined functions stored along with the variable type. Why not use them?? In your case is more suitable to access count /length method instead of testing the first value.

An if clause sometimes take more time than a predefined function.

On the first look seems ok to store the counter but imagine you will have to update the array. You will have to do 2 operations, one to insert other to update the counter. So 2 operations means 2 variables to be changed. For statically arrays might be ok to have them counter then the list, but for dinamic ones NO NO NO. On the other hand please read programming basic concepts and you will find your idea as a bad one, not complying with programming principles.