Can mixing/adding two band-limited signals create any frequencies above Nyquist?
Ideally no, adding 2 signals should result as a simple sum.
provided you don’t clip
DSP systems have finite dynamic range. A double float has a very large dynamic range so it is not usually a consideration.
Fixed point arithmetic has uniform quantization but the finite dynamic range requires attention.
Floating point is not a uniform quantization, so arithmetic also introduce rounding, which are discontinuous on small scales.