It's a good start, then maybe you will at least be able to figure out that suggestions like those made by @violet3an really make no sense.
The problem is total current.
70mA per motor, at max PWM.
About 500mA max for the ULN chip.
One motor per ULN output is a lot safer for the ULN chip.
A PCA output can drive more than one ULN input...
Leo..
70mA x 8 = 560mA
It is not clear if OP ever wants to drive all motors the same time at 100% PWM.
Yes, I want this. The idea is to be able to control all 16 motors with individual PWM, but it could happen that all motors will work at a given time at 100% PWM
According to the datasheet 500mA is the collector current per driver. For the total current you must look at the power dissipation. At 100mA you have a max Uce of 1.1V = 0.11W per driver. So 0.88W with 8 drivers. The max powerdissipation of the chip is 2.2W.
There should be no problem to operate 8 motors at max speed (70mA) with the ULN driver.
Will this will solve the issue with the ULN chip - to use a separate mosfet for each motor?
(motors 9 - 16 are not in the picture)
btw - motor wire should be long - around 5 - 10 meters
You know that the MOSFETs are surface mount parts (SMD).
Do you know how to solder them.
yes. but I might will use a through hole misfit instead.
Will these MOSFETs be fast enough to do 0-100% PWM at your selected PWM frequency?
to be honest I don’t know regarding the AOD424, but the FQP30N06L should be fine from what I see in the forum and the web
edited schematics:
I’m not sure if I should ask it in a new topic -
which AWG size I should use in order to solder a longer cable for those small mini vibration motors? is 26AWG is fine or I should go different size?
What will be a good practice to solder them in order not to detached easily?
Can the nano supply enough current to the PCA9685 module?
What is the purpose of connecting VCC1 to V+?
Will PWM still work with a capacitor across the motor?
How do you know that those MOSFETs are fast enough?
Yes.
I am not sure, This is what I was told here at post #2
Will PWM still work with a capacitor across the motor?
from what I have seen it should work with 100nF
The capacitor's job is to "filter noise". Whether its value is good or not depends on the PWM frequency, because it definitely slows down the rise and fall of the PWM signals. If these cause the square signal to become trapezoidal or triangular, it can cause problems. You need to look at it on an oscilloscope!
What noise?
Well then I guess you are all ready to go.
I think I am gonna learn the hard way.. (which is good, I guess) 
I don't like the sound of that
what should be appropriate for using long wires with those small dc motors and arduino?