First. You have not activated your IBF account. Please click on the link in the mail you received from the forum admin in your mailbox. Failure to do so will cause all your posts go into moderation.
Now to your queries and understanding:
a) When you take a new connection with broadband, you are liable to pay installation charges on two accounts - one for landline and other for broadband. Each charge, I believe, is Rs. 250/-. You got a waiver off the BB installation charge. So there is no anamoly there.
b) BSNL's BB usage charges, fees, etc. are always prorated unless you opt for an unlimited plan. So if you opted for Home 250 plan and plan got activated on 19th of the month, you will be charged from 19 till 30 or 31 (as the case may be). The BB fee of Rs. 250/- will not be charged in full but prorated for the 13 days. Likewise, the usage limit is also prorated.
c) But if you opt of unlimited plan (UL750 or UL1350), there is no prorated charge. You are charged in full for the entire month, regardless of the start date and you can download as much as you like.
Yes. It is a pity that they do not explain these things when you take the connection. It is only after getting the bill, that people realize things. Same confusion is on night time free usage also (2 AM to 8 AM). Please read the many articles and guides posted in the
Broadband How to section.