If I install the newest version 7.5.6 on my server with PHP 4.4.X and MySQL 4.1.X and later moving it on a server with the newest versions of PHP and MySQL, could there be a problem ? Or is it working well afterwards ?
Should be no issues. The only potential issue would be is if you were moving from a windows to a linux server. Then you might have some problems with the MySQL tables and the upper/lowercasing