What “i.e.” and “e.g.” actually mean, you start to see how they are distinct. Specifically, “i.e.” is an abbreviation for the Latin “id est”, more or less meaning “that is”. “E.g.” is an abbreviation for the Latin “exempli gratia”, meaning “for the sake of example”, or the short version, “for example”.
As a general rule, if you can substitute in “for example” where
you've used “e.g.”, you are probably using it correctly. Likewise,
if you can substitute in “that is” where you are using “i.e.”, you
are also probably using it correctly.
The key distinction, with “e.g.” you are stating one or more
examples, with “i.e.” you are not talking about anything but what
you specifically say.
It is a mistake to include an “etc.” after an “e.g.” list, because
“et cetera” is implied, so it shouldn't be included at the end of
such a list.