Yes, you have it correct but it is not critical. Any vinegar will work but the recommended apple cider vinegar brings a whole lot of new nutrients into the mix. The dosage of 1 tablespoon per gallon is just a starting suggestion... you may need more or less. Non cooked shells should not be used for it will take forever for them to ferment... you will find that even after thorough cooking, many of the insides are still whiteWhat do you mean by 5 parts of vinegar, for example, if I have 100 grams of egg shells. I should add 500 grams of vinegar? Can I use any vinegar?
Also, about the one spoon per gallon, is that for any size plant? Will too much hurt?
About heating the shells. You say that the white ones will be a phosphorus source, are you saying I should put a few aside and not cook them?