Tom35,
the senario you depict will result in NEGATIVE pressure differential (where the cabin pressure is less than the ambient pressure)
B18210,
The positive pressure relief valves will open when cabin pressure excedes a given value. Nominal max diff is around 8.6 psi for most commercial a/c. In the event of a failure of the pressurization system there are relief valves fitted which will open to prevent over-pressure (typically 8.8-8.9 psi diff)
Reasons for them opening would be for example a system failure or an error where the system is left selected to manual and the system outflow valves were closed (in this case as the a/c climbed the cabin altitude would remain at or below take-off elevation and eventually the max diff would be exceded).
Your second condition has nothing to do with pressurization. At a guess you are being given conditions which would lead to an overspeed situation.