There isn't a quick/easy of removing all soft-deleted threads. Yes you can do it with queries but it requires updating various tables and then the caches have to be rebuilt.
Moderator log length can be set in Options -> Logging Options.
You can remove all entries by truncating the xf_moderator_log table.
Administrator log length can be set in config.php. How do I change the number of days for which the Admin Log in the ACP is retained?
Edit the library/config.php file and add the following: