The limiting bank angle will depend on a large number of things, speed and airframe being the major ones. If you are teaching PPL studes then 30 degrees might be appropriate. If you are on instruments I assume you're familiar with the formula for R1 bank angle. Anything else can be found in the standard FI manuals.
Yes, crosswind is "max demonstrated" and not a limit. It is perfectly possible to operate beyond max demo with a range of techniques, including differential thrust.
HFD