Rajab

Q: An uncle told me that “… if you fast in rajab Allah Ta'ala on the day of judgment will give you a drink from His own hands from the river of Rajab which is whiter than milk sweeter than honey…”

I did some research and didn’t find any Hadith claiming this and I found out that there isn’t any evidence to back there being a specific reward for fasting during Rajab. I didn’t respond to his text to avoid trouble. My family is South Asian and bidah/cultural practices are rife.

Q: What is the significance of Lailatul Raghaaib which is celebrated on the first Thursday of Rajab?

Q: 

1. Is it true that in the month of Rajab it is more sinful to commit sin and the reward also more?

2. What should one do specially in this month?

Q: The following info has been taken from AL-GHUNYA LI TALIBEEN by Abdul Kadir Jeelani(r.a). There is a special salaat to be performed in the month of rajab, this salaat can be performed after maghrib or ishaa, this salatul haajat makes up a total of 30 rakaats, it is read in 3 stages: first 10 rakats are read between the 1st and 10th of rajab. The second 10 between 11th and 20th of rajab, and the last 10 between 21st and 30th of rajab. The niyyah is am reading 2 rakaat salatul haajah O Allah for the sake our master Mohammed Sallallahu Alaihi Wasallam with the birth of whom you have illuminated the entire world and the for the sake of your auspicious month rajab grant me relieve from the troubles of this world and the hereafter. Its read in 2 rakaats each in both rakaat you should read allhamdu, 3x suratul kaafirun and 3x suratul ikhlaas, its better if its read on a friday or monday night. So i have read 20 rakaats in the first 20 days but now I have gotten my periods and by the time I'll be paak it will be Shaaban so is it ok if I read the remaining 10 rakaats in the month of Shaaban although in the niyyah it says shaaban?...Because I don't feel like leaving it incomplete.