As I've written many times in the public support tickets (which can be searched and read even by non-subscribers like you) this is caused by wrong permissions on your site causing a directory to not be copied. There is a bug in Admin Tools' plugin, causing it to fail with a fatal error when that directory isn't copied. It was discovered because some other users, unlike you, took the time to file a free bug report in our Pre-Sales forum, supplying me with adequate information to replicate the issue and solve it. The bottom line is, if you have a bug report, please report it on our site. It's free. Unless you report it, don't expect to see it resolved.
Anyway, the solution to your problem is rather simple: extract the installation archive and copy the fof directory inside your site's libraries directory, so that you now have a libraries/fof directory.
Besides, we have manual uninstallation instructions in our release announcement page (https://www.akeebabackup.com/home/news/56-releases/1446-admin-tools-2-2-0.html). If you follow them, the software uninstalls cleanly and doesn't cause the problems you mention. My guess is that you removed the component but not the plugins, hence the persistence of your problem.
Finally, please note that as stated in the release announcement and our download page, Joomla! 1.7 is NOT supported.