I was going to run 9-20v through it, controlled by 3.3v. But I don't know what limitations the difference between N and Z(I have it) series imposes (what resistors to use, and whether this model can handle such a load)
You have not said what load you will be controlling (ie how many amps of current). Since you will be using 3.3 volt control logic the N option seems appropriate. 20 volts is not a problem as both options can handle up to 55 volts. As for the gate resistors, see the picture for reference.
No problem. Also, the transistor has a very low on-resistance and you won't need a heatsink with this package (TO220). However, if you are going to use PWM control at a high enough frequency, you may need to use a heatsink and/or gate driver.
I think 8 bits and 16 bits of PWM are not very big, right? And the same lack of problems for 3A, 15-20v and uselessness of TO220 in the Irlb3034 series mosfets and the IRL3705N transistor?
This is PWM resolution, not frequency. The IRLB3034 is overpowered for the purpose and its gate capacitance is quite large, which can lead to potential problems even at low PWM frequency if no driver is used.
Thank you very much! Then how can I understand, depending on the frequency, at what limit the suitable mosfets start, for example, for 80Hz, 1kHz, 64kHz, etc.?
For example, irlb3034 does not even heat up even under a 100A current when operating from 3.3 V, but such transistors must be inferior in some way to those that only output 5A (IRL3705Z) from 3.3v and those that start operating only from 10V?