Is there any difference between it running in 8086 mode, 80286 mode and 80386 mode? Does it use more features or bigger register to calculate things when those newer processors are chosen during the setup?

Edit: I've tried both 8086 and 80386 mode, and both seem to run without many problems. 80286 mode probably also works.

Maybe it's just using more RAM when selecting the newer CPUs(using HIMEM.SYS)?