How can I send api calls from my plugin?

You can check this:

$api_endpoint="https://url_to_API";
$api_args     = array(
   'method'  => 'GET',
   'headers' => array( 'Accept' => 'application/json', 'any' => 'other' )
);
$queries      = array(
   'your_query'   => 1,
   'another_query'   => 5,
);

$api_endpoint = add_query_arg( $queries, $api_endpoint );
$response     = wp_remote_request( $api_endpoint, $api_args );
$response_code = wp_remote_retrieve_response_code( $response )
$data      = json_decode( wp_remote_retrieve_body( $response ), true );

Also you can access to the response code in this way: $response['response']['code'];

I didn’t try it but I have found this resources I think it can be usefull for you:

add_query_arg()

wp_remote_request()

wp_remote_retrieve_response_code()

wp_remote_retrieve_body()

Hope it works for you 🙂
I am waiting to know if it has worked correctly for you, because I think is a very interesting issue.