A replica 386 would be impractically large - it's got around 275k transistors, compared to the 3.5k in the 6502. At the same scale as the MOnSter 6502, that'd be about a hundred square feet of PCB.
The number of layers isn't even remotely close to being a constraint. The real i386DX was manufactured on a process which only supported two metal layers, and a PCB version isn't subject to the same constraints as silicon.
The ARM1 was a 32-bit CPU and it only had about 25K transistors so that one might be fair game if you can bring the components a little bit closer together, but you don't need a fancy PCB for that, and I guess the clock speed would need to be very slow if it's several square feet in size.
Components like transistors usually have to go on the surface of a PCB. (While there are techniques for embedding components in a PCB, they're extraordinarily expensive and would not be feasible for a project like this one.)
Probably not, because transistors produce some heat, and you can't really sandwich surface mount transistors between PCB layers either. You could vertically stack PCBs with some spacing, however, but then normal PCBs will do the job.
It is possible to embed components in the middle of a pcb, but it's a pretty specialist process (read: a pain in the neck because it interleaves the pcb fabrication and assembly stages, making both steps more complicated).
The number of layers isn't even remotely close to being a constraint. The real i386DX was manufactured on a process which only supported two metal layers, and a PCB version isn't subject to the same constraints as silicon.