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Idle curiosity very welcome!
1) That's a Brompton rear light bracket that I use to mount a rear dynamo light. It's far from perfect but it works well enough.
2) That cable you're seeing is the wiring for that same rear dynamo light. The derailleur cables are standard and run to stops on the downtube.
Edit: just realised what you mean, and yes that is the rear mech cable running under the head tube... I threw the bike together late one lockdown night and messed up the cable routing there. I was intending to fix it but obviously never got round to it before dismantling the thing. Can't imagining doing it this way would be overly detrimental but it wasn't intentional.
It looks lovely, but much to small for me.
Idle curiosity: