it mean you are about to give birth or tou are full
Yes, "burst with curiosity" is a common idiom that means to be extremely eager or interested in learning or finding out about something. It conveys a strong sense of excitement and anticipation.
I was bursting with curiosity means a character bursting with energy and vivacity. If you are bursting to do something, you are very eager to do it.
Think of being so full of curiosity that you explode - that's the image in this phrase. It's not an idiom, though - it's just an exaggeration.
Curiosity killed the cat.
Don't be too curious!
No, it's an advertising slogan.
It is an idiom or turn of phrase that generally means to immediately start crying.
It is very likely that "curiosity killed the cat" is meant rather than "care killed the cat". That idiom means that being curious is sometimes dangerous.
It's not really an idiom. It means "what are you thinking about."
It is not an idiom, it means your nose is itching.
RFP is not an idiom. It's an abbreviation.
"Sieve" is not an idiom. See the related link.