What happens when many interrupt requests happen at the same time?
In most cases, interrupt requests are processed, in priority order. Typically this does not involve a queue, but instead, lower priority interrupts continue to be asserted until such time as they can be processed. 

A typical example would be the interrupt controller in a PC. This traditionally has a number of inputs, each assigned a priority. The peripheral signals its request. This remains until the processor clears the interrupting condition.