Book about technical and academic writing

Solution 1:

Nicholas Higham's book Handbook of writing for the mathematical sciences is detailed, clear, and overall very useful. He covers all the four bullet points that you have raised. Moreover, he gives an annotated reference to useful style guides, technical writing guides, dictionaries, and so on. I am sure you won't be disappointed!

Edit: I guess you might already be familiar with the classic: The Elements of Style by Strunk & White --- this book is a gem on writing, and is worth reading again and again every few months.

Finally, here is a paper with very practical advice. This paper really underscores the importance of structure, and offers concrete advice on how to attain good structure: The Science of Scientific Writing, by G. D. Gopen and J. A. Swan. The fundamental thesis of the paper is: Writing to meet the reader’s expectation.

Solution 2:

A set of lecture notes from a course on mathematical writing run by Don Knuth http://tex.loria.fr/typographie/mathwriting.pdf

Solution 3:

I found Krantz's A Primer of Mathematical Writing helpful, though not deep.

Solution 4:

How to write mathematics is a free essay by Paul Halmos which fulfills your first three criteria. It is short, but has several good points.

Solution 5:

Here is another: Handbook of Writing for the Mathematical Sciences - Nicholas J. Higham.