Localhost website to Linux shared server : PHP error/warning

Question

I did a website on my Windows pc Localhost and everything working fine. I just uploaded my website on a shared Linux server and I see many error/warning in the error_log file that I do not understand.

PHP Warning:  session_start(): Cannot send session cache limiter - headers already sent

The first thing I do in all files is :

<?
  session_start();
  ...

Second warning:

PHP Warning:  mysql_real_escape_string(): Access denied for user 'root'@'localhost' (using password: NO)

The second thing I do in all files is to open a connection with the BD

<?php
    session_start();
    require_once('bdservice.php');

    $bd = new BDService();

I don't understand why I have no error in LocalHost and now I this...