Forget old server ... focus on new.
"i think i'm installing with softaculus then replace the file(moodledata, web & database)...... so, should i reinstall it manually?"
'I think'? Uhhhh ... best if we know, isn't it?
So you used Softac to install a 4.2 site ... then replaced your backups (code and moodledata) to what/where Softac did it's thing. IF Softac installed a 4.4 and your backup is a 4.2 ... there could be issues IF you didn't completely wipe out the contents of what Softac did.
Should you reinstall it manually ... YES! it's not really an install ... it's a 'migration' ... where you know where document root is for nginx and your code archive un-compressed goes there. In nginx/config.php of moodle code there is a path to moodledata directory. moodledata directory has to be readable by nginx/moodle code but one should not be able to use a browser and go directly to it.
Did you review the Moodle Doc link I posted earlier on nginx?
Just viewed your site ... it's messed up ... strongly suggest adding a line to config.php to force the theme to boost.
$CFG->theme='boost';
Add that line above the comments in that file that say:
// There is no php closing tag in this file,
// it is intentional because it prevents trailing whitespace problems!
Do not have to restart server or any services, just go to the moodle via browser and hopefully the site will look better than it is now!
'SoS', Ken