It rather depends on what I'm doing. If I'm stirring a cauldron and making a cup of tea at the same time, it tends to be rather noticeable to anyone watching, though how much I'm paying attention is variable. If the potion itself requires magic then I'll know it was done. I tend to concentrate on what I'm doing under those circumstances unless it is a truly mundane potion that I've brewed a thousand times. Those potions I could brew half-asleep or even half-dead. The Priori incantatem and veritaserum, as well as the mandatory hour long hold for Polyjuice, tend to mitigate some of the more egregrious problems but if the Ministry itself is corrupt, then the Wizengamot generally follows. Unknown on the Wolfsbane front. Lupin himself takes it and he offered it to the other werewolves but they either weren't interested or refused to accept the precautions I wished to take.
Actually magic tends to short out most technology. Why do you think the Muggleborn students don't use it at Hogwarts? Radios and gramophones are simple enough to work through it but televisions and computers certainly don't. I have been able to short out even SHIELD's technology while I've been here though I'm unable to speak of the specific circumstances. But yes, attempting to sneak past my wards may be unpleasant.
Not quite the Library of Congress but I am using my memories to access my library at home and at Hogwarts, as well as the Hogwarts library, Albus' books and on one occasion, Lucius' library. And it is somewhat cumbersome even if I am using a copying spell.
Many magical people would be appalled at the idea of attempting to explain magic to Muggles so your grandmother is in good company. And that's not even taking into account the rather more purist element who would be a good deal more than appalled. Your grandmother is, however correct. Many things go into the construction of a potion, not just the ingredients and the method.