Hi Paolo, how about someone prying into your affairs instead of just minding their own business? Also, one could poke their nose into something that doesn’t really concern them. Both have a little negative connotations and mean someone being rather too curious or inquisitive.

If it is a bad thing, then we say "He sticks his nose in everybody's business" or "He sticks his nose where it doesn't belong." If it is a good thing, we might say "He has a very inquisitive mind." If a person always asks a lot of questions, we might say "He is going to grill you about this." (Ti metterà su una griglia.)

Hello. You can be inquisitive or have a "thirst for knowledge". A famous idiom is "curiosity killed the cat" but that's not of a warning not to look into other people's business than a desire to know things. I hope this helps!