I'm an English teacher first (30 years' experience - 14 of them with scientists and engineers) and developer second, so I often find it relatively easy to grasp what a non-native speaker is trying to ask without always feeling confident enough to answer the technical points posed in the question. In these cases, my most useful contribution is to improve the way the question is phrased in the hope that some whiz kid out there can provide the technical answer. What is involved in the review process, and how long might it typically take?
As for the review process itself, I can only comment on how I do it.
If the edit clears up all the issues I see within the question/answer, I'll accept it. If the edit leaves serious problems within the content then, even if the edit itself is good, I might reject it. Usually I go to the question myself, improve it and judge how much time it has taken me to do so. If this is significantly more than the other editor will have spent, I might just mark his edit as "not helpful". If you glanced over a minor issue, no problem. I'll correct it and mark your edit as helpful. Moral of that story: Don't just fix one minor thing, fix the entire content.
With regards to code edits, things become slightly more complex. Editing code in the question itself is usually a big nono, apart from something like indentation corrections. If I feel your edit changes the question or might actually hide the OPs problems, I'll reject it.
Code edits in an answer I only handle when I'm confident of their correctness or appropriateness. If edits of such content are so significant that I can't judge it with a simple review, I might leave it alone, or reject it along the lines of "should have been an answer instead".
Whatever you do, don't make the fact that you've edited a question, part of the question itself. If your edit is brilliant, but you leave something like "Edited by me for clarity" or if you even add a whole separate section with an "edited version" of the content, I will reject it. (Though I have the rare nice day where I actually go to the question to remove the fluff you added). Edited content should appear as if written by the OP.
As for the comments you received on only editing those questions which won't be closed outright anyway, please do so. When the edits appear in the review queue, I am not filtering them out anymore based on the quality/appropriateness of the question itself. So if you edit something which should not be on this particular Q&A anyway, I will review it. The review queue is often full as it is anyway, so please don't add to that by editing bad/off-topic content.
With regards to the average time taken between the suggested edit and final acceptance or rejection, I have no hard data. I have handled edits mere seconds after they were suggested, but have also seen some which hung around for several hours (though this is less likely with the new review queues). If the suggested edit is substantial enough that its evaluation requires specialist knowledge in a topic, it might take some time. If the edit is not merely a spelling correction (or something similar) then I usually stay away from them if they are not in my area of expertise. Such edits might take a little longer to get evaluated.
What I've taken away from this discussion and Bart's excellent answer
I don't know if an answer is the right place for the following summary, but I'm exploring this whole process so here goes in case it helps other newish collaborators like myself:
Levels of Intervention
There seem to be many layers of editing that different contributors are comfortable with.
I will be attempting levels 1 and 2 for the time being, especially with obviously non-native speakers. I have no great ambitions to get involved at levels 3 and 4.