The Doctor doesn't like his real name mentioned. He has quite a substantial case of compounded PTSD that he represses enough to function, and is seeing Dr. Deane about it. He's also wacky as heck anyway. Delirium might have known his sixth incarnation (http://en.wikipedia.org/wiki/Sixth_Doctor) well enough.

Sara Sidle is explicitly not insane (it's one of her worst fears, that she might be), but her mother was--she went mad and killed Sara's abusive father. Sara has thus spent time visiting institutions and nearly died (http://www.crimelab.nl/transcripts.php?series=1&season=5&episode=21) while investigating a case in one within the last year, her time.