A. No. The LSASS process will cache pages as they're requested, but there's no way to pre-cache the entire database. Obviously, over time more of the database will be cached as more pages are read.
This raises an interesting operational point. Because the AD database is cached over time, every time you reboot your domain controller (DC) that cache is lost and has to start all over again. You may want to reconsider that weekly backup of your DC.
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