I was always told to grind them before you include them. Makes them absorb faster.

don't breathe the dust and don't spark a flame if the dust poofs while working it. It can be volatile if fine enough

vinegar creating calcium carbonate (?) and use them as a calcium tea?

Plenty youtubes on the subject.

buy organic eggs and now that I have accumulated some, and the weather is turning, I wanted to make sure Fall was the right time

into nutrients. You should not have any problem even if you have enough crushed shells to use as mulch. The calcium carbonate provides for a quicker intake for the plants and unless you're gardening through the winter like I am here in Florida you'll be fine.