In a ‘free’ (or uncoupled) turbine engine (specifically the Rolls Royce C20-250), what is spinning the compressor blades (N1) after start? It can’t be N2, because it’s a free turbine. I don’t think they’re freewheeling, because otherwise how would I get bleed air? And I’m pretty sure the combustion chamber is ahead of the N2 stack, so N2 wouldn't have its own compressor wheel and if it did, I wouldn't have clean bleed air.
In a C20-250 engine the compressor section is driven by the high pressure turbine (Ng spool, not N1) independent of the power turbine. The power turbine drives the gearbox and subsequently the output shaft via a concentric driveshaft to the gas core spool.
I believe you’re confusing the configuration of this engine by assuming that all free turbine turboshaft engines are laid out similar to a PWAC PT-6 engine. While the PT-6 design certainly excels in terms of simplicity as well as modularity for ease of maintenance, it is not necessarily the only configuration for free turbine engine. Plenty of other free turbine turboshafts have other unorthodox layouts but all operate according to the same principles.
A cutaway of the C20-250 engine appears below. Note the non-axisymmetric air channel carrying air from the last stage of the compressor section to the aftmost part of the engine for introduction into the single can-type combustor.
It's a turboshaft engine, so almost all the power from the gas stream is converted into rotary power for the output shaft. All the power, minus the power required to drive the compressor. The HP turbine drives the compressor (N2), the LP turbine drives the output shaft (N1).
what is spinning the compressor blades (N1) after start?
The gas stream hitting the HP turbine is.