None of those are inconsistent. If a is confusing for you, use i, A and o, that'll be enough for most things you want. Most of the time you'll drop into insert mode through cw, cib and the like anyway.
What do you mean by empty lines? Does your vim somehow have lines in the buffer that aren't in the file?
The point is that they teach you that 'i' enters insert mode and '<esc>' exits it. This is not true! It it was true and 'i' and '<esc>' only switched mode, then the sequence 'i<esc>' would have no effect. Instead 'i<esc>' leaves the cursor on another character.
I think the parent poster meant that two newlines in file are displayed as an empty line. That's ok. What's odd is that the cursor is allowed to stay in the empty line, as if it was on a virtual character at the end of the line. However, if the line is not empty, the cursor is not allowed to go one character right of the last one.
What do you mean by empty lines? Does your vim somehow have lines in the buffer that aren't in the file?