I’ve read that line from Parks and Rec was unscripted and improvised by Chris Pratt
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Yeah, according to the writers of the episode. They said they got kind of angry because they couldn't think of anything funnier than that line. To be fair, it's fucking hysterical. Pratt might be a shitty person but he's witty as shit.

I thought it was more that there is only one of him so there is no statistically significant sample size of shape shifters.
I think the medical scanner basically reads odo as a calibration error.
Second in his class at Starfleet, you know. Would have been first, if he hadn't chosen to give a wrong answer on that question about preganglionic fibers vs postganglionic nerve, to avoid getting caught for genetic manipulation.
Presumably, the good doctor won those medical awards for impeccable excellence in the field of bedside manners.