OK, I can address those questions.
The EF86 is the first stage, so the signal is very small and it will dominate the tube-rush noise. In the classic textbooks, noise is primarily covered for radio frequencies where shot noise dominates. (Shot noise is basically the electrons hitting the plate at random times, and is pure white noise, equal energy per unit bandwidth.) Pentodes are about 3-4 dB noisier than triodes for shot noise, which has earned them a reputation for being noisier in general. But at audio frequencies, Blencowe has shown that 1/f noise generated in the cathode coating of emissive material dominates. This noise is inversely proportional to frequency, and dominates below typically 10kHz, so there is little to choose between them. The 1/f noise depends on the details of the cathode coating and the impurities in the metal sleeve, and is hard to predict. The EF86 earned its reputation for good sound by its use in studio microphone preamps, so you might expect it to sound good in a phono preamp - and it does.
On the other hand, the first stage has low distortion because the signal is small, and distortion falls with signal level - especially higher-order distortion. Distortion is dominated by the second and last stage, the 6922. It still has substantial headroom so the distortion is small and mostly second harmonic.
Power supply noise is substantially reduced by the 12AU7 high-voltage regulator, and further reduced by the current-source plate loads. It has no discernible effect on noise or distortion.
That leaves ground noise, microphonics, and radio-frequency interference (RFI) to round out the list of common noises. The EF86 has an internal shield, as well as the external shield used in Eros, to address RFI; it is also designed for minimal microphony. (Ground noise is not dependent on tube selection.)
