I have two questions related to STM32L443CCY6TR microcontroller which I do not understand clearly.

Powering the microcontroller from a battery

The STM32L443CCY6TR microcontroller can be powered from a battery as it has a wide operating voltage range from 1.8V to 3.6V.

Suppose battery is a single-cell lithium-ion battery, which typically provides a voltage range of 3.0V to 4.2V.

Can we connect the battery to the VDD pin of the STM32L443CCY6TR directly or need to use regulator?

 

If the battery voltage is 4.2V you would be exceeding the maximum operating voltage of 3.6V.
You can try placing one or two 1N4001 series diodes in series with the battery.

 

It is advisable to use a voltage regulator to regulate the voltage of the battery to a stable level that is within the operating voltage range of the microcontroller. This will ensure that the microcontroller is not damaged due to overvoltage.