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I don't think there's anything legally forbidding you to do any of those things (well, the EKG thing is weird, but I dunno if it's forbidden). You should list them as part of your job. I took medical histories as part of one of my volunteer experiences.
And to sort of extend this question to shadowing experiences that involved more than just standing in the corner passively observing.
In addition to some of the other important things I learned from shadowing, I also know what an enlarged prostate feels like?

plz don't start a year early. go have a drink or watch a movie or something