General Requirements
- Book
- Conic Sections
- Triange Geometry
- Inconics of Triangle
Ideal Topics
- Projective properties arising from inconics like collinearity/concurrency relationships
- Other basic properties (e.g. foci are isogonal conjugates)
- Important points corresponding to inconics (e.g. Brianchon Point)
- Special inconics
- Equations in various angular or linear coordinate systems (e.g. Trilinear Coordinates, Barycentric Coordinates)
Probably the most celebrated of the old books in English is Salmon's Treatise on Conics. An earlier answer has download links to that and some other 19th century English analytical geometry texts:
Good books on conic section.
Another place to look is volume 2 of H.F. Baker's treatise, http://archive.org/details/principlesofgeom02bake .
I don't think that most of the subjects listed in the question are necessarily covered in those books, but they would contain most of the classical facts, especially if supplemented with a detailed enough source on projective geometry.
More: following the comment link at an earlier question ( Existence of Gergonne point, without Ceva theorem ) and looking on MathWorld leads to some references related to the question. Smith, Geometrical Conics seems closest to what you are asking (of the books) and there are some journal articles.