The flyback diode is oddly positioned but I doubt if that matters in a simulation. It is the same with that 150R current limiting resistor which is also not optimally positioned.
What is the specification of that motor in Proteus ?
The IRLZ44 is not what I would call a "logic level" MOSFET, but it will work fine with 5V Arduinos and medium current (up to 10A) motors. You always need to look at the data sheet, for example at this plot from the IRLZ44 data sheet:
With your gate voltage being critical place R1 on the other Side of R2, it is acting as a voltage divider. I am assuming the 10K is to guarantee the state of the MOSFET truing setup etc. until your code gains control.
Edit. I took another look and I had R1 and R2 backwards. Usually the first component is 1 but you have it the other way around.
R1 limits the amount of current drawn from the IO pin when activating the transistor. At 5v that would be about 33mA here. Without R1 it could potentially draw enough to damage the IO pin. Once saturated, the transistor could stay energized from internal capacitance so a path to ground is needed to bleed that charge.
Unless it's for a high frequency signal, the off time trailing isn't a huge issue here. I'd actually go higher on the resistance values. Maybe an R1 of 1k and R2 of 1meg depending on the transistor specs. @jremington would probably be better to comment on specific values though.
What transistor? I see a MOSFET that draws current when the gate is being turned on or off to charge/discharge the capacitance, Miller being one of them. Once on or off it will not draw any current other them maybe pico amps because of leakage. The schematic in 9 is correct. The 10K R1 is there to determine the state of the output pin while being reset until your code sets it up. R2 helps prevent oscillation, I prefer 50 Ohms but higher will work, just slows the turn on/off which will cause the MOSFET to dissipate more power. In this case it does not matter. The processor has a rating to allow for capacitive loads where this should not exceed that rating even if connected direct to the gate.
The IRL Z44N is in fact a logic level gate drive mosfet. I know, I am using one myself to drive a 12v automotive relay. I have left it in test mode switching the relay on and off every 5 seconds for 4 hours without fault.
Confused on how your claiming this is not a "Logic Level" MOSFET?
You also claim its only good for 10A motors when it is rated for a continuous drain of up to 47A and a pulsed drain of 160A
Perhaps we are looking at 2 different IRL Z44N Mosfets??