how to avoid inserting the same primary key and values in php mysql

First let me say, that you shouldn't use your code in production, because you can use it for sql injection. But for learning, you have to possibilities to solve this issue:

1. Check first if the movie already exists in your database, by an additional query:

   SELECT * FROM movie where movie_name=$movie

2. You set an unique constraint on the movie_name column. But then you have to be sure, to check if the insert query does not fail:

   ALTER TABLE movie ADD CONSTRAINT movie_name UNIQUE (movie_name);

But the best way is, to use the unique constraint and check if the movie already exists.

Edit1

You have to check if the actor and the movie already exist in the tables. if they exists you must fetch their id (actor_no, movie_no) from the database:

$dbc = @mysqli_connect('localhost', 'root', 'black98765', 'activity_7b')
OR die("Could not connect to MySQL: " . mysqli_connect_error());

$actor_query = "SELECT * FROM actor where name='$actor'";

$actor_result = mysqli_query($dbc, $actor_query);
$actor_data = mysqli_fetch_array($actor_result, MYSQLI_NUM);

$actor_no = null;

// Check if actor already exists
if ($actor_data[0] > 1) {
    // Actor already exists in the table, so we get just the primary id from the existing
    $actor =  mysqli_fetch_assoc($actor_result);
    $actor_no = $actor['actor_no'];
} else {
    // Actor does not exist in the table, so we will create a new entry
    //insert into actor table
    $q = "INSERT INTO actor (name) VALUES ('$actor')";
    //execute the query to get primary key value
    $r = mysqli_query($dbc, $q);
    //assign to variable below
    $actor_no = mysqli_insert_id($dbc);
}

// Do the same with the movie ...

This code is not perfect (sql injection) but it should solve the issue.

UPDATE Debugging the code shows me, that there were more issues than expected, Wrong column names... . With the following code it should work:

<?php
$dbc = @mysqli_connect('localhost', 'root', 'black98765', 'activity_7b')
OR die("Could not connect to MySQL: " . mysqli_connect_error());

$actor_query = "SELECT * FROM actor where name='$actor'";

$actor_result = mysqli_query($dbc, $actor_query);

$actor_data = mysqli_fetch_array($actor_result);

$actor_no = null;

// Check if actor already exists
if (isset($actor_data['actor_no'])) {
    $actor_no = (int)$actor_data['actor_no'];
} else {
    // Actor does not exist in the table, so we will create a new entry
    //insert into actor table
    $q = "INSERT INTO actor (name) VALUES ('$actor')";
    //execute the query to get primary key value
    $r = mysqli_query($dbc, $q);

    if ($r) {
        echo "Inserted actor successfully!";
        //assign to variable below
        $actor_no = mysqli_insert_id($dbc);
    } else {
        echo "Failed to insert actor data!";
        mysqli_error($dbc);
    }
}
//insert into movie table
$movie_query = "SELECT * FROM movie where movie_name='$movie'";

$movie_result = mysqli_query($dbc, $movie_query);

$movie_data = mysqli_fetch_array($movie_result);

$movie_no = null;
// Check if movie already exists
if (isset($movie_data['movie_no'])) {
    $movie_no = $movie_data['movie_no'];
} else {
    //movie does not exist in the table, so we will create a new entry
    //insert into actor table
    $q2 = "INSERT INTO movie (movie_name, release_year) VALUES ('$movie',DATE_FORMAT('$year','%Y-%m-%d'))";
    //execute the query to get primary key value
    $r2 = mysqli_query($dbc, $q2);

    if ($r2) {
        echo "Inserted move successfully!";
        //assign to variable below
        $movie_no = mysqli_insert_id($dbc);
    } else {
        echo "Failed to Insert Data!";
        mysqli_error($dbc);
    }


}
if (null !== $movie_no && null !== $actor_no) {
    $q3 = "INSERT INTO movie_actor (movie_no, actor_no, rate) VALUES ($movie_no, $actor_no, '$rate')";

//connect and insert $q
    $r3 = mysqli_query($dbc, $q3);
    if ($r3) {
        echo "Inserted Successfully!";
    } else {
        echo "Failed to Insert Data!";
        mysqli_error($dbc);
    }

} else {
    echo "Failed to Insert Data!";
}
mysqli_close($dbc);
?>

Hope it work now.