The Falstad-Simulator can be a useful tool, especially for those people who are just starting-out,

BTW if you have a better simulator to propose me I'm all ears!

 

Most of the time, on simpler Circuits, I won't even bother with a proper PCB, ever.
A "Vero-Board", AKA, "Through-Hole-Boards", and about ~75 other names for
a PCB-Board with Copper-Plated-Holes laid-out in a "Grid-Pattern" covering the whole Board,
will do just fine in a "permanent" application,

I guess it depends where you live and how conveniently/at what price you can get custom PCBs.
I live in China and here it takes just two to three days to get a custom PCB made and a couple of dollars. For seven more dollars you even get the professional steel mask if you want to semi mass produce your boards.
It's pretty hard to beat that kind of service

 

Does that Price include populating the Board with Components ?, Wow !!!

As far as Simulation-Software goes,
and even though there's a fairly steep Learning-Curve,
and even though I don't use it myself due to that Learning-Curve,
"P-Spice-for-TI" is Free-Software that is probably the most widely used and accepted
Simulator amongst the regular-contributors here in these Forums.
There may be other Free-Versions of P-Spice that I'm not aware of,
the Link is for the Texas-Instruments-version.
.
.
.

 

Does that Price include populating the Board with Components ?, Wow !!!

For two dollars you only get the PCB alone, but you can get it with the components soldered for extra money. The price is calculated according to the component price+a fixed fee per component (I don't remember how much but its pretty cheap). I don't know how big of a price difference there might be between the chinese version of the website and the foreign one.
I had a few other boards assembled by them and it wasn't expensive at all, the only small issue is that they don't always have every component available in stock.

The final quality is great, I have no complain about their service. This time I decided to solder the components myself, so I only got the PCB made as well as the steel mask (wasn't absolutely necessary, but it made applying the soldering paste a lot quicker). Then I just had to put the components using tweezers and use my little reflow oven to solder everything. Pretty easy, and it works great...if you don't invert the mosfets and the transistors, of course...

I'm not sure if I'm allowed to mention it here, but the service I used was JLCPCB (I'm not working for them and I'm not affiliated in any way, just a happy customer). You can do 100% of the work online, you start by designing your circuit in EasyEDA which is an online circuit designer, then you route your circuit, and then you can click on a button to order the circuit directly from there. They have pretty much every possible option to do every kind of circuit you want up until 20 layers.
I think their service is available outside of China as well, but I don't know how long it takes to deliver. You can have a look at what price it would take to make a board you designed here, just input your gerber file and select the options you want, it's pretty fun to do.

As far as Simulation-Software goes,
and even though there's a fairly steep Learning-Curve,
and even though I don't use it myself due to that Learning-Curve,
"P-Spice-for-TI" is Free-Software that is probably the most widely used and accepted
Simulator amongst the regular-contributors here in these Forums.
There may be other Free-Versions of P-Spice that I'm not aware of,
the Link is for the Texas-Instruments-version.

Great I'll check that, thank you!

 

BTW if you have a better simulator to propose me I'm all ears!

Several of us use the free LTspice simulator from Analog Devices.
It has a somewhat steep learning curve, but that are many sample simulations and on-line tutorials to help, as well as asking questions here, which will usually be answered.

 

For reliably switching in my LTspice sim, I had to increase C4 in your circuit to at least 20µF.

And once again you were right!
At first I put a 10uF and it still wasn't enough.
Unfortunately these were the biggest capacitors I had available in the shop, so I put another one in parallel and now it seems to work great!

Now there is still one little issue remaining: I noticed that there is a big voltage drop at the final diode, which takes away power from the fan. Because of this sometimes the fan struggles a little bit to start from time to time.
Is there a diode with a lower voltage drop I could use?

 

I noticed that there is a big voltage drop at the final diode, which takes away power from the fan.

So what's the purpose of the diode?
I see no useful purpose for it in this application.

A Schottky diode has a lower forward voltage drop.

 

So what's the purpose of the diode?
I see no useful purpose for it in this application.

A Schottky diode has a lower forward voltage drop.

The purpose of the diode is to prevent the back EMF from the fan's motor to go back into the circuit when I try to power off.
I can confirm it is necessary because I tried bypassing it and it became impossible to turn off the circuit.

Would a schottky diode achieve the same result (allowing forward current to pass but stop back current) with minimal voltage drop?
How do I choose a suitable one for my application (I never used schottky diodes before so I don't really know how they work) is there any drawbakc or thing to consider?

Thanks again for your patience!

 

Schottky diode is doped differently. it works just like regular diode but forward voltage drop is lower (also max reverse voltage is lower too). that makes difference when load needs precise voltage or when current is sufficient - lower voltage drop means less power wasted as heat. but for small fan i would say it works so don't bother...
but if that bothers you, you can simply use another transistor (much lower voltage drop). pretty sure the problem will go away if you try larger capacitor too or use shorter presses.