It's hard to say what's part of the lens and what's part of the postprocessing - notice that the pictures of the lens/camera itself is quite warm also. May just be the author's style.
Early BW films were mostly sensitive to the blue and green side of the spectrum. Only later did they become more sensitive to the entire visible spectrum (including the red zone, which we consider warmer). They were called panchromatic films (as opposed to earlier orthochromatic films).
Agreed, but not surprising... calling a nice modern lens "warm" would be nearly an insult. Modern lenses generally prioritize accuracy to warmth, and appropriately so. It is however a little sad that there is such a small market for more stylistic lenses.
It is perhaps sad from a nostalgic standpoint, but otherwise it is quite possible to closely approximate all characteristics of an old lens just by post-processing an image taken with an accurate modern lens (e.g. the Hipstamatic app), so it is little wonder that the market for old, stylistic lenses is so small.
I used to have a mobile phone which could take "warm" photos. It could also do "alien vision", and a couple of other neat tricks. People said it was cheesy. You can also attach some APS-C lenses to a Full Frame, and get "romantic" vignetting. If you do that in Photoshop, it's fake. The "creamiest" bokeh you can get is a gaussian blur, unless they know it's photoshopped and then it's no longer "creamy".
There's some kind of emotional response people have to optical distortions which they don't have if they know it's from post-processing.
