Why I can't get twice the input voltage from a double voltage circuit and how I can solve this?
4) You have stated that you must use LM741, but for future reference, your application calls for a voltage comparator. For example, a LM393, which is from the same era as the LM741, would not give you the same issues.

Given that you are stuck with the LM741, something like the schematic below should work for what I think is your application. And it is simpler and does not require any negative voltage.







simulate this circuit &ndash; Schematic created using CircuitLab


  In this way both output states allow to turn the transistor on, such as V+ = 5-1.6 and V- = 0+1.6


This quote seems to imply that you have V+, the positive supply pin, connected to 5V. But the opamp inputs can be 5V or higher, so V+ needs to be higher, like +12V.

Also, from the TI datasheet, the LM741 minimum operating voltage is +/- 10V. That means it needs 20V to operate per the datasheet. But I am going to guess that 12V is probably good enough for this.

3) The capacitors as shown does not get reversed voltage during normal operation.