Travelling with type D (Multi) sticker Visa

I have an Italian type D (Multiple entry) study visa valid until August 2023. I entered Italy on October 2022.


Am i allowed to travel to my home country ( Outside EU ) and Enter again to Italy without resident permit, only with entry sticker visa that attached on my passport?


Is the immigration ask me about resident permit?


Can i enter any other Schengen state with this Sticker visa ?


Thanks for kind information.