Swap MOSFET from a Module Driver

Hi, I'm working on a vacuum cleaner robot and I'm trying to figure out some hardware alternatives for a guide found on instructables.

Some Info:
board: Arduino UNO
battery: 12V 1.3Ah 25C LIPO
blower fan: 12V 4.5A (MAX)

IRF520 module driver(*1): this is an obsolete MOSFET. The IRL8113 seems to be a good alternative for my needs.
I searched the MOSFET according to this user advises, is it a good pick?

Now, since I've already the MOSFET module driver linked(*1), can I only buy the new MOSFET and replace the IRF520 from the board with it or I've to wire the new MOSFET to a new circuit board?

Thanks.

6 milliohms will handle upto 15A or so without needing a heatsink, although switching losses need to be
factored in, the IRL8113 should handle this OK.

You also need a suitably rated free-wheel diode across the blower motor....

Hi, thank you.

I was thinking about this schottky diode SB530-E3/73. It suits my needs? Is the schematic ok?

Yes looks OK - but learn to draw schematics, not wiring diagrams, schematics explain, wiring diagrams confuse (they are only ever useful for wiring up a circuit by rote). Learn the symbols for components, these are the true language of electroncis!

You would be very wise to add a 10k -- 100k resistor between gate and source to prevent premature conduction of the MOSFET at power-up, and protect from static damage.

Yes I know, I'll learn .
What do you think as a first approach (free online software) ?
note: I used a zener diode instead of schottky because the last one was not implemented in the software.

I also found that post that talk about a mosfet + flyback diode + gate resistor for the same problem.
Which is better (also in terms of components availability) ?

Yup, that's a circuit! Use a standard silicon diode symbol for the freewheel diode though.

The gate resistor mentioned in that thread is probably a low value one to limit current from the Arduino pin,
150 ohms is plenty for that - some MOSFETs are very capacitive loads and will pull large currents when directly connected to Arduino pins, beyond the datasheet limits. IRL8113 capacitance is effectively about 6nF (infered from total gate charge at 4.5V).

This is the final schematic:

I just realized how expensive are the shipments of online electronics components distributor...
So I found these from eBay Italy, are ok?

Can I place the order?