No, that's not safe! Lime juice is very acidic - it could cause diarrhea and a bad diaper rash, never mind mess with her digestive system. Citris fruits are typically not recommended until after one YEAR old. At 1 month, your baby should not be given ANYTHING other than breastmilk. Stop the lime juice, stop the gripe water. It is NORMAL for some breastfed babies to not have frequent bowel movements. Breastmilk is easy to digest so her body just doesn't have much waste to get rid of. Your baby is just fine, so stop messing with her. Breastfeed on demand and she will be fine!
Yikes, what? NO From Dr Jack Newman, probably unarguably the world's foremost expert on infant feeding: Some breastfed babies, after the first three to four weeks of life, may suddenly change their stool pattern from many each day, to one every three days or even less. Some babies have gone as long as 20 days or more without a bowel movement. As long as the baby is otherwise well, and the stool is the usual pasty or soft, yellow movement, this is not constipation and is of no concern.
I dont know about time, but I think its too acid. You can try a lil bit of orange juice disolved with water, that helps ;) or prune juice with water.
Ummm....no that's not really safe. I read your question earlier, and we all assured you a breastfeeding baby is able to go up to 10 days without pooping. It's not a problem unless she's in pain.