I'd been mulling over possible responses to this thread as the subject was once close to my heart. In my case, I drew a lot from the groundwork laid during my days as a literature student, many years ago. I applied methods adapted from literary analysis on a variety of anime I enjoyed and, to my surprise, I found many who responded positively to my views, even when I was being harsh.
I decided in the end that there's not much need to go into a detailed response to your specific questions — others have already given fine answers that echo what I would have said. Suffice to say that I learnt a long time ago that there is no one approach to critical analysis any more than there is just a single approach to creating art. The tools that a critic uses may be similar to those of another, but the conceptual framework he applies would be uniquely his own.
What I also know, from experience, is that examples of superb analysis help build appreciation of what needs to be done far better than multi-page treatises on esoteric technique. There are many people uniquely gifted with the ability to do mental gymnastics on abstract details; there are far, far more people — ordinary people like you and me — who much prefer dealing with the concrete, the plain-and-simple imagery we encounter in our daily lives.
Because, when you can visualise the argument in your mind's eye, that is when understanding is achieved. So, take a gander at how Roger Ebert approached his analysis of one of the most highly respected films in anime:
He makes it look easy, almost effortless. The best artists and critics usually do. The irony, of course, is that there is nothing easy or obvious about the process, yet it
simply works. Why?
Because:
1) He uses a great 'hook': Ebert states from the outset that he enjoyed the movie and expresses it in everyday language ("I was moved... just about to tears.") That is, quite simply, his "hook", that all-important introduction that piques the viewers' interest. (Ebert's interested? Really? Why? I must find out more.) He doesn't gush nor feign enthusiasm. He just tells it as it is, without harping on his points or talking down to his audience.
2) He serves his audience, not his ego: Ebert explains
everything he lays out. He never assumes that his audience knows the kinds of things he knows about film art and its history. He goes the extra mile to explain the context of Japanese anime to Western viewers more familiar with the technical sophistication of Disney animation. And he never once lapses into jargon, except when it was necessary to explain his point, such as with regard to differences in frame rate between anime and cartoon.
3) He adds value by providing insight: And that insight is uniquely his own, a product of his accumulated knowledge of art history, both Western and Japanese. For example, he relates multiple scenes from the movie with the "pillow words" of Japanese literature, coining his own words — "pillow scenes" — to help viewers visualise the similarities. For the vast majority of people with no prior knowledge on the subject, such pointers are immensely helpful and may even spur some to find out more on their own.
4) He doesn't shy away from his own opinion: Ebert offers his own genial objection to those who may be turned off by the perceived technical deficiencies of anime, by reminding his viewers that, in the end, such things "simply become stylistic details that are less important as the film goes on. You're not looking on the whole film on the basis of some abstract idea of technical excellence. You're looking at it in terms of its excellence as art. And art doesn't depend on how many frames per second, on whether this was done or that was done. It depends on how it makes you feel".
Particularly on that final point:
There is no such thing as objective analysis when it comes to reviewing art. How can it possibly be, when it "depends on how it makes you feel"? So, don't fall into the trap of trying to be "objective", to be "unbiased" — that is a fool's game, the sign of someone who is not confident about his opinion.
Of course, you can always be proven wrong, sometimes very embarrassingly so. In which case, eat humble pie, try harder next time and never, ever forget that criticism is a two-way street.