Import nested JSON to MySQL with relations using php

Below is a fully functional transactional pdo process for your exact case. I've tested on my server with 3 MyISAM tables that match your structure. Now, it is possible that you are not into pdo at the moment; if not, I hope my offering will compel you to try something new and modernize the way you query your database.

$json='[
    {
        "targetgroup": "Staff",
        "plan": "this field just exists and should be ignored in database",
        "budgetlevel": "Government",
        "spots": 5,
        "edutype": "Bachelor",
        "qualilevel": "Specialist",
        "speciality": "Mathematician",
        "qualification": "Finished",
        "faculty": "Applied mathematics",
        "institute": "this field is sometimes empty in input data",
        "eduform": "Full-time",
        "profiles": [
            "Jr. Arithmetic manager"
        ],
        "entrancetests": [
            {
                "subject": "math",
                "typeoftest": "GOV",
                "minscore": "37",
                "ratingtype": "out of 100"
            },
            {
                "subject": "language",
                "typeoftest": "GOV",
                "minscore": "27",
                "ratingtype": "out of 100"
            },
            {
                "subject": "physics",
                "typeoftest": "GOV",
                "minscore": "40",
                "ratingtype": "out of 100"
            }
        ]
    },
  {
        "targetgroup": "Educational workers",
        "plan": "fridge",
        "budgetlevel": "Legacy",
        "spots": 26,
        "edutype": "Bachelor",
        "qualilevel": "Master",
        "speciality": "Data analysis",
        "qualification": "Finished",
        "faculty": "Machine learning mathematics",
        "institute": "",
        "eduform": "Full-time",
        "profiles": [
            "Head counting manager"
        ],
        "entrancetests": [
            {
                "subject": "Discrete mathematics",
                "typeoftest": "GOV",
                "minscore": "32",
                "ratingtype": "Out of 100"
            },
            {
                "subject": "Algorythm theory",
                "typeoftest": "GOV",
                "minscore": "51",
                "ratingtype": "Out of 100"
            },
            {
                "subject": "Advanced exception catching",
                "typeoftest": "GOV",
                "minscore": "56",
                "ratingtype": "Out of 100"
            }
        ]
    }
]';


$db=new PDO("mysql:host=yourhost;dbname=yourdbname;charset=utf8","username","password");

try{
    $db->setAttribute(PDO::ATTR_ERRMODE,PDO::ERRMODE_EXCEPTION);  // this will deny subsequent queries from being executed if there is an error and permit exception handle at the bottom
    $db->beginTransaction();

    // dep
    $dep_cols=array("targetgroup","budgetlevel","spots",
        "edutype","qualilevel","speciality","qualification",
        "faculty","institute","eduform");  // declare columns
    $dep_keys=array_map(function($v){return ":$v";},$dep_cols);  // build :keys    
    $dep_cols=array_combine($dep_keys,$dep_cols);   // assign :keys
    var_export($dep_cols);
    $dep_query="INSERT INTO `dep` (`".implode('`,`',$dep_cols)."`)"; // list columns as csv
    $dep_query.=" VALUES (".implode(',',array_keys($dep_cols)).");";
    echo "<div>$dep_query</div>";
    $stmt_add_dep=$db->prepare($dep_query);

    // profile
    $profile_cols=array('name');
    $profile_query="INSERT INTO `profile` (`id`,`".implode('`,`',$profile_cols)."`)"; // list columns as csv
    $profile_query.=" VALUES (LAST_INSERT_ID(),".implode(',',array_fill(0,sizeof($profile_cols),"?")).");";
    echo "<div>$profile_query</div>";
    
    // entrancetests
    $entrance_cols=array('subject','typeoftest','minscore','ratingtype');  // declare columns
    $entrance_keys=array_map(function($v){return ":$v";},$entrance_cols);  // build :keys
    $entrance_cols=array_combine($entrance_keys,$entrance_cols);  // assign :keys    
    var_export($entrance_cols);
    $entrance_query="INSERT INTO `entrancetests` (`id`,`".implode('`,`',$entrance_cols)."`)"; // list columns as csv
    $entrance_query.=" VALUES (LAST_INSERT_ID(),".implode(',',array_keys($entrance_cols)).");";
    echo "<div>$entrance_query</div>";
    $stmt_add_entrance=$db->prepare($entrance_query);
        
    foreach(json_decode($json) as $d){
        foreach($dep_cols as $k=>$v){
            $stmt_add_dep->bindValue($k,(property_exists($d,$v)?$d->$v:""));
            echo "<div>$k => {$d->$v}</div>";
        }
        $stmt_add_dep->execute();
        echo "<div>Dep Affected Rows: ",$stmt_add_dep->rowCount(),"</div><br>";
        
        $stmt_add_profile=$db->prepare($profile_query);
        foreach($d->profiles as $k=>$v){
            $stmt_add_profile->bindValue($k+1,$v);
            echo "<div>",$k+1," => $v</div>";
        }
        $stmt_add_profile->execute();
        echo "<div>Profile Affected Rows: ",$stmt_add_profile->rowCount(),"</div><br>";
        
        foreach($d->entrancetests as $o){
            foreach($entrance_cols as $k=>$v){
                $stmt_add_entrance->bindValue($k,(property_exists($o,$v)?$o->$v:""));
                echo "<div>$k => {$o->$v}</div>";
            }
        }
        $stmt_add_entrance->execute();
        echo "<div>Entrance Affected Rows: ",$stmt_add_entrance->rowCount(),"</div><br>";
    }
    
    // $db->commit();  // Only use with InnoDB tables.  MyISAM is auto-commit
    
}
catch(PDOException $e){
    // $db->rollBack();  // Only works if InnoDB table.  If MyISAM table, it doesn't rollback.
    echo "Error message: {$e->getMessage()}. File: {$e->getFile()}. Line: {$e->getLine()}";
    // do not show these error messages to users when you go live
}

As is, this script will stop executing subsequent queries if a query has an error.