Disclaimer: These are some of the materials that I came across, some of which I used routinely and others as references. While the resources don't cover all the things OP mentioned, these are worth to study.
$\bullet$ Analysis and Design of Experiments, H. B. Mann, Dover, $1949.$
Author does an exceptional job in keeping the chapters short but detailed enough to not create any void in derivations. The book is not voluminous; though sometimes beating the bush to go to the main results but this is definitely not quaint: a sharp exposition. The highlights are the chapters on latin squares, Galois fields and Orthogonal Latin squares. More or less self-contained.
$\bullet$ Mathematics of Design and Analysis of Experiments, M. C. Chakrabarti, Asia Publishing House, $1962.$
These are collection of lectures by the author. Not recommended for first reading. The materials are terse. I liked his treatment of confounded arrangements in split-plot designs, application of Galois fields and finite geometry in constructing the confounded designs, hypercubes of strength $d.$ But again, I reiterate it is not for first reading.
$\bullet$ Constructions and Combinatorial Problems in Design of Experiments, Damaraju Raghavarao, Wiley, $1971.$
The author indeed has largely been successful in consolidating some of the important topics: construction of orthogonal arrays, products of orthogonal arrays, embeddings, MacNeish-Mann Theorem, duals of incomplete block designs, partial geometries. Essentially a formal treatment of the field: a good read.
$\bullet$ Optimal Design: An Introduction to the Theory for Parameter Estimation, S.D. Silvey, Chapman and Hall, $1980.$
My personal favorite. Silvey did an amazing job in writing such a beautiful treatise. If one knows nothing and wants to have an intuitive idea about information matrices, design criteria, $\mathcal D$ optimality, design algorithms, then without an iota of doubt, do read this classic.
$\bullet$ Optimal Design of Experiments, Friedrich Pukelsheim, SIAM, $2006.$
This is a magnum opus in true sense for it delves deep, I mean way deep, in covering optimality theory. It thoroughly discusses information matrices, optimality criteria, the equivalence theorems, $\cal D,~A, ~E, ~T$ optimality, Bayes designs, invariant designs, Loewner and Kiefer optimality, rotatibility.
$\bullet$ Design and Analysis of Experiments, M.K.Sharma, B. V. S. Sisodia, PHI Learning Pvt. Ltd., $2012 . $
A beginner's book with a copious writing style and a tolerable pace develops the finite field theory, finite geometries, difference sets and their applications in constructing the requisite designs. Exercises are easy to moderate.
$\bullet$ Robust Response Surfaces, Regression, and Positive Data Analyses, R. N. Das, CRC Press, $2014.$
The monograph provides a conspicuous elucidation of weak rotatibility, slope rotatibility, weak slope rotatibility, $\mathcal D$ optimal slope rotatibility, and also brief discussion of correlated structures. Although the main attention and emphasis are on robust response surfaces. It is replete with good applications.
