Driving P-MOSFET with Netduino
In general, simulating your design should answer that. Free tools like LTSpice or Qucs can be used for the simulation. 
The limiting resistor is good practice. The pull-up resistor does not limit current drawn from the microcontroller pin to the Gate. This current may spike beyond the MCU's pin maximum if directly connected, for charging the 1.4 nF input capacitance of the FET. A 180 Ohm resistor will be sufficient to limit pin current to under 28 mA, safe enough for many MCUs.   
No. The Transfer Characteristics graph indicates a Vgs of around -6 volts required to saturate this FET, for Vds = -30 Volts. For Vds = -5 Volts and Vgs = -4 Volts (not -5V, see next point), the On-Region Characteristics graph indicates a current of well under 2 Amperes.
It should, as the rated minimum Vgs.th is -2 Volts, while the voltage divider formed by the 2 kOhm pull-up and the 500 Ohm current limiting resistor gives Vgs values of -1.36 Volts and -4 Volts respectively for MCU pin high and low. The problem you will face is at the pin=low part.
Yes. The maximum switching cycle (turn-on + turn-off) for FQP27P06 is (45+380+70+190)=**685 nS**. Thus worst-case switching frequency is around 1.46 MHz (Vdd = 30 Volts, Rg = 25 Ohms). Allowing a hefty margin for the much lower Vdd = 5V and the 500 Ohm current limiting resistor, 15 KHz switching is definitely safe to aim for, much higher than the target of 100 Hz.