Indeed!
I'm planning a visit to the Domus Aurea in the spring and I'll be more than happy to post pictures!I'm looking forward to it as you can also experience a reconstruction of the Villa with augmented reality goggles.
Sure, very interesting! As far as I know Alta Semita was indeed a wealthy residential area in Republican times, and also during the Imperial period. I am no archaeologist but I remember reading that the 3rd cohort of the Vigiles in ancient Rome was located roughly in today's Piazza dei Cinquecento, so not exactly where the Vigili del Fuoco's HQ is located today (Via Genova). They are actually a part of the Ministry of Internal Affairs.
The Castra Praetoria were located between the Viminal Hill and the Esquiline, and the Central Logistics Grouping of the Italian Army (Caserma "Castro Pretorio") is still there, so there is definitely some continuity with its ancient past!
As far as Santa Pudenziana is concerned, I wonder if there are any archaeologists reading this who could help shed some light on its past. Apparently the thesis according to which the church had been built over a thermal complex is now being questioned, in favour of the original one claiming that the church had been built on the domus of senator Pudens.