record data in different tables

It could be adding a switch to generate the query depending on the role

$query="";
switch($trol)
{
  case 1:
    $query="insert into Estudiante() values()";
  break;
  case 2:
     $query="insert into Profesor() values()";
  break;
  case 3:
     $query="insert into Acudiente() values()";
  break;
}

Simplifying the fields a bit for a more compact response, let's say that your tables have fields correo and nombres in addition to the primary key that is auto-incremental and you do not need to insert it explicitly. That said, you have three problems:

For point 1 , you should wrap everything up in a check:

if(!isset($_POST["trol"],$_POST["tcorreo"],$_POST["tnombres"])) {
  echo "<br />". "No ha enviado todos los campos." . "<br />";
  echo "<a href='index.html'>Por favor complete todos los campos</a>";
} else {
  // tu lógica acá
}

For point 2 , you should use another field (such as email) to know if the user already exists

For point 3 , the first thing would be to cast $_POST['trol'] to an integer and then see if the role exists between your dictionary rol => tabla

$diccionario = [
 1 => 'estudiante',
 2 => 'profesor',
 3 => 'acudiente'
];

$trol = (int) $_POST['trol'];

if(!array_key_exists($trol, $diccionario)) {
   echo "<br />". "Ese rol no existe en el sistema." . "<br />";
   echo "<a href='index.html'>Por favor escoja otro rol</a>";
} else {
  // tu lógica
}

When you cast it you make sure you do not insert into the table an arbitrary string that could lend itself to an SQL injection. If the role exists in the dictionary you can get the name of the table from it, which you will inevitably interpolate in your sentences. But at least you handle the dictionary so that interpolation is harmless.

Done the checks, you can already do:

$mysqli = new mysqli(DB_HOST, DB_USER, DB_PASSWORD, DB_NAME);
$correo = $_POST['tcorreo'];
$nombres = $_POST['tnombres'];
$tabla = $diccionario[$trol];

$stmt1 = $mysqli->prepare("SELECT correo from $tabla WHERE correo=?");
$stmt1->bind_param("s", $correo);

$stmt1->execute();

$stmt1->store_result();
$count = $stmt1->num_rows;
$stmt1->close();

if($count > 0) {
   echo "<br />". "El email de Usuario ya ha sido tomado." . "<br />";
   echo "<a href='index.html'>Por favor escoga otro email</a>";
} else {

  // lógica de inserción

}

Then we got to the point where you checked that:

• The role exists in your dictionary
• The fields were populated in the form
• The email is free in the table you get from the dictionary

So you apply the insert:

$stmt2 = $mysqli->prepare("INSERT INTO $tabla (correo, nombres) VALUES (?, ?)");

$stmt2->bind_param("ss", $correo, $nombres);
$stmt2->execute();
$stmt2->close();

Putting everything together and rearranging so as not to have so many nested if:

$mysqli = new mysqli(DB_HOST, DB_USER, DB_PASSWORD, DB_NAME);

$diccionario = [
    1 => 'estudiante',
    2 => 'profesor',
    3 => 'acudiente',
];

$trol = isset($_POST['trol']) ? (int) $_POST['trol'] : 0;

if (!array_key_exists($trol, $diccionario)) {
    echo "<br />" . "Ese rol no existe en el sistema." . "<br />";
    echo "<a href='index.html'>Por favor escoja otro rol</a>";
} else if (!isset($_POST["trol"], $_POST["tcorreo"], $_POST["tnombres"])) {
    echo "<br />" . "No ha enviado todos los campos." . "<br />";
    echo "<a href='index.html'>Por favor complete todos los campos</a>";
} else {
    $correo = $_POST['tcorreo'];
    $nombres = $_POST['tnombres'];
    $tabla = $diccionario[$trol];

    $stmt1 = $mysqli->prepare("SELECT correo from $tabla WHERE correo=?");
    $stmt1->bind_param("s", $correo);

    $stmt1->execute();

    $stmt1->store_result();
    $count = $stmt1->num_rows;
    $stmt1->close();

    if ($count > 0) {
        echo "<br />" . "El email de Usuario ya ha sido tomado." . "<br />";
        echo "<a href='index.html'>Por favor escoga otro email</a>";
    } else {

        $stmt2 = $mysqli->prepare("INSERT INTO $tabla (correo, nombres) VALUES (?, ?)");

        $stmt2->bind_param("ss", $correo, $nombres);
        $stmt2->execute();
        $stmt2->close();

        echo "<br />" . "Todo funcionó: Usuario creado en la tabla $table." . "<br />";
    }

}

This script lacks checks to handle cases where you can not connect or the statements are executed poorly, but that is your task.