I've written only two reviews, because I only review stuff that I connected with strongly. You can find them on my profile: http://webfictionguide.com/shelves/dnsantana/ they might help you, though I tend to do somewhat long, verbose stuff and I don't want to seem like I'm promoting that exclusively. You can totally write short pithy reviews if you want, I think that can be done right. I can't do it though.
With all that in mind, here's my answers to those questions.
I don't think you have to read all of the story. Almost every serial will keep going for a while, and your review will only ever be of "the latest chapter I read," unless the author stops or you wait what could be a long time until it's over. As an author of a serial myself, I'd rather people not wait to review, since I plan to keep going for a long time. So read a chunk, and then review. However if you have strong criticisms of the story, you should probably disclose how much you read, so that people understand the context of your criticism.
As for how much you should read: if the story is just starting, like there's only 5-6 chapters or something, you might as well read it all. A story in this format is probably still getting its legs at that point so you might as well see as much as the author's got to deliver. If it's really long when you decide to start reading and review, then ten or fifteen updates should give you some idea of what the writing is like, though you should be clear that you don't know the whole story at that time.
Personally, I don't follow things update to update. I wait until there's a big chunk and binge it. Both stories I reviewed, I knew I was going to review them about two or three chapters in because the plots really captivated me. At that point, I kept reading mostly because I was entertained, rather than for review purposes. I stopped to review when I felt I had enough bullet points to cover.
I don't really have a set structure for reviews. I write a first draft that's just a list of stuff I've been aggregating that I found interesting in the story, and what I post on the site is that list fleshed out more and arranged so it reads better and isn't just a bunch of bullet points. I tend to go heavier on what people do right than what they do wrong. I feel like I want people to play to their strengths, because the weaknesses I perceive are probably up to individual taste. I mention criticisms, of course, but I tend to focus on what I believe the story was trying to do and what it accomplished in that realm.
Some basic lit things you can cover: writing style, 1st or Third Person, or something funky? What do you think it accomplishes? Viewpoint character or characters and your opinion on them, what their stories are, what themes you think the author is trying to hit. Genre, and how the author fits into one or subverts it (or multiples). Meta stuff like the layout of the website, update length, update frequency, any bonus content setups the author's got, and things like that. Remember though, that you're also talking to readers, not just to the author. Try to give the reader a good sense of what the story is.
Beyond that, you just have to develop your own style. I've been reviewing things for a long time. I used to work for a couple of gaming blogs, and I'm basically always thinking about things I consume, so I've got a list of things I look for, and it's hard to convey how to write a good review, because media tends to draw out reviews from me, rather than me sitting down and forcing one. Hopefully though the above ground work stuff can help you start and give you things to think about.
As the one being reviewed, I'd hope to get someone's perspective on what they think I'm doing. I'd like your personal opinion, drawn from your own self, and framed in whatever way is honest to you. I think perception is important and valuable and hard to acquire; I'd like to know what people are seeing when they read and what they take away from it. I'm less interested in stuff that can be patched up easily, like typos. I'm more interested in stuff that's hard or impossible to patch up, like if you think a character is boring and I've spent a third of the text following that character.