It is really needed to use 2 batteries for this robot?

Hi.
It is a good practice to separate the feeding from arduino (control) and from dc motors (power).

Do you think it is strictly needed in my robot?

POWER:
Lipo 3.7 300mAh
2 micro servo 9gr. They should drain 150-200mA per one when working.
They go at derated voltage of 3-4.2v are driven by the motor drive

CONTRL
ARduino pro mini 3v3
Accelerometer adx345 for tilt sensing (the robot move overr the windows)
Motordrive tb6612fng
Ir for edge detection

I don't know if is a pure case but if a i use pololu motor driver and pull out the mini drivers inside the servos i saw more much less noisy over accelerometer readings.

The bot don't need to do difficult path and the terrain (glass of tbe winwows is smooth) so current stay quite stable.

How do company projects theyr robot, such as drones and robot cleaner?

A large part of electronic circuit design includes learning how to deal with the question you raise, and is called "power supply decoupling".

Robot manufacturers employ trained engineers to make sure circuitry is properly designed and functions correctly before production, or it will fail.

If you want your robot to work properly and don't want to take the time to learn about supply decoupling, use separate batteries for the servos and the Arduino.

From your specifications, that battery has too little capacity for your robot.