Pro Mini 3.3V, ULM2003 - output voltage is too low

Do You mean that I should use the values from this scheme:

Should I conclude that when the resistor's value (going from PWM pin to MOSFET's gate) is lower, then the voltage between each side of the motor can be higher?

No. That 100ohm resistor has no effect on the mosfet/motor.
It's just there to limit Arduino pin current during the very short switching pulses.
Leo..

What parameter tells me the level of voltage (gate - source) that fully opens the drain? Gate Threshold Voltage? I need to fully open the drain on IRL540N with 3.3V output from Arduino Mini. Is this possible?

What parameter tells me the level of voltage (gate - source) that fully opens the drain? Gate Threshold Voltage?

Yes. Another factor for drain current is RDS(ON).

I need to fully open the drain on IRL540N with 3.3V output from Arduino Mini. Is this possible?

No.

What do You think about IRLML6344TRPBF?

Yes, this will work much better with 3.3V.

Another possibility might be this.

I don't understand it. If gate - source voltage threshold says about the level of fully opening the drain current, why 3.3V won't fully open IRL540N (V gate-source threshold = min. 1.0V, max. 2.0V)?

I don't have any space for 4 additional breakboards, that's why I want to use only MOSFETs without it.
I have an acces to IRLML6344TRPBF. Would it let the drain current be fully open or there are others that would? It's very important for my application to fully open the drain current.

You don't seem to be "grasping" the problem.

The battery is 3.7V. The Pro Mini needs AT LEAST 3.7V.

As soon as you turn on the ULN driver, the driver drops 1V , the motor drops the rest of the voltage (2.7V) and both of them load down the battery , reducing the Vcc or Vin for the Pro Mini.

Neither the Pro Mini nor the motors are going to get enough voltage because the ULN is a BJT and has a large voltage drop (high RCEON voltage. You need a low RDSON mosfet and a separate battery for the Pro Mini.

My previous post is about IRL540N and IRLML6344TRPBF. I'm not using ULN anymore.

majk92:
I don't understand it. If gate - source voltage threshold says about the level of fully opening the drain current, why 3.3V won't fully open IRL540N (V gate-source threshold = min. 1.0V, max. 2.0V)?

Vgt (gate threshold) is the voltage that the fet just starts to conduct. Twice that voltage might be needed to turn the mosfet (almost) fully on. You might have a mosfet with Vgt of 2volt.
Did you measure the voltage across the mosfet and battery as I asked you in post#17.
That will tell you if the volt drop problem lies with the mosfet or the battery.
Leo..

An 8 MHz 3.3V Promini will work happily at 3.7V to 5V. Connect power to the VCC pin instead of the RAW pin, that bypasses the regulator.
AOI514 would work fine for that motor. Very low Rds, and Logic Level gate (as low as 2.4V to turn it on I think)

AOI510 has even lower Rds.

That means the battery is dead and might even be toast, as it was overdischarged.

I haven't seen any response to this comment yet. Do you understand that you cannot discharge a 1S Lipo below 3.2V without damaging it ?

The fact that the drop across the motor was 1.6 V doesn't (by itself) mean anything about the voltage across the battery because you didn't post the voltage across the mosfet so we can't make any assumptions about Vmotor + VDSmosfet = X => X < 3.2V but we can say that in order for VDSmosfet to be 1.6V with an RDSON of 0.044 ohms, IDS would have to be 36A, and that seems unlikely with the motors you are using. (V= I*R => I = V/R)

Draw your own conclusions...