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The message you get means that there is no user with an ID of 62 on your site. Since the scope of this feature is to change the default Super Administrator user ID from 62 to something else, there is nothing to do. The "JUser::_load: Unable to load user with id: 62" is normal. When you launch that feature, we ask Joomla! to check if there is a user with an ID of 62. When there is not, Joomla! throws this error message (which can not be suppressed). It's confusing, but it's normal.

That makes sense. This error message only appears when the default user (ID=62) is completely deleted. If it is just renamed and disabled -what Admin Tools does- Joomla! doesn't complain and prints no error message. In both cases, your site is equally protected, though :)

I am also pro-prevention. Curing happens when it's too late.

That said, the major question is not what the attacker did to your site, but how he did that. The former allows you to cure the symptoms, the latter allows you to cure the root cause. Since you had a malicious script uploaded to your site, the most probable causes are:
- Unsafe permissions (e.g. 0777 in a web accessible directory).
- Unsafe ownership, e.g. all files and folders owned by the user the web server runs under on a shared server.
- A vulnerable script which allows upload of arbitrary PHP files, with easily predictable names, in a web accessible directory
- Stolen FTP and/or hosting account credentials, e.g. due to malware or social engineering

All of these are easy to prevent, at least in a large degree. As I always say, there is no point believing that you can make your site unhackable. There is no such thing and whoever says that is a dangerous fool. What you can do is to harden your site, making it more difficult for an attacker to succeed. Unless you are a highly valuable target (like a bank, CIA, NSA or NASA) this is enough to force an attacker to stop wasting too much time on your site and move on.

I have written up a guide to unhacking and hardening your site. I recommend starting by reading it and apply the hints contained therein.