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You can remove both .htaccess files (site root and administrator).

However, I believe that the problem is that you do not have a configuration.php file.

Did you transfer the site using Akeeba Backup? If so, did you have any errors during the restoration? I believe that you got a message that the configuration.php file cannot be written but you may have dismissed it without following the instructions on that page (which is totally human, given that 99% of the times restoring a backup it is merely a matter of clicking Next without as much as reading what each page says).

Hm I don't know but you're totally right that tehre is no configuration.php.

That's the only root cause of the error message “No configuration file found and no installation code available. Exiting...”. You will see it comes from Joomla's administrator/includes/framework.php lines 19 to 33.

This time the file manager didn't succeed to erase the directories but the rest of the files got erased, so I have also an issue that I hope my host will fix soon or else I will have to

So, is it possible that there were leftover files from a previous Joomla! version? That could explain the 403 in the frontend, but I can't think of why you'd be getting the error in the administrator if you do have a configuration.php — unless, of course, there's something going wrong at the host's side (e.g. the Operating System's or PHP's file stat cache is not being cleaned, something I'd seen a decade ago on some misconfigured hosts using OpenLinux when memory got tight).

You're welcome!