If you don't have a scope, and say you "don't know how the circuit works", you need to do more learning about DC-DC converters, and maybe basic electronics as well (not sure what you know)
No, you must use a MOSFET where the rated gate voltage (ie, a gate voltage for which a current and on state resistance is specified - not gate threshold voltage, which is much lower). The IRF3205 is not suitable for 5v control - you must get one with a "logic level gate" (you can filter digikey mosfets based on logic level gate - there are many options).
Is it a fast switching schottky? Be sure to get one that is speced as fast switching (typically these will specifically mention suitability for use in DC-DC switching power supplies in the datasheet)
Layout matters in switching regulators. Wires/traces carrying high current need to be kept short. Look at the designs of the chinese ones, how they have the traces around the inductor, diode, and switch as short as possible.
I made it:
1) Because i need to know how it works, how it behaves and i'm going to learn about it
2) Chinese converters are awful, i need powerful and trustful (i know diy is not always the best solution but beats cheap badly made Chinese things)
1) Well, there's going to be a lot of learning in your future then. You might want to do more of that before you continue building. There are many good books on DC-DC converter design, as this is a challenging discipline that is very important in industry. There are also tools available to simulate DC-DC converters, which may be useful. You also probably need to learn how to use PCB design software, since DC-DC converters are layout sensitive.
2) Then use the pololu ones, or the fancy ones from digikey? Quite frankly, the chinese crap ones work surprisingly well considering that they cost less than a cup of coffee shipped - I use them all over the place, and the only time I've had problems with them is when I shorted out converters without short circuit protection.