Does the ऐनीमे follow the मांगा story line accurately?

Yes it does , make sure आप watch to प्यार ru trouble and the ova as well in the following order.
1 to प्यार ru
2 ova
3 trouble
A little bit of info is left out in the transaction between ova and trouble but आप should be fine.

As for मांगा after all the ऐनीमे there is a sequel called to प्यार ru darkness , this one is highly ecchi and I personally don't recommend it.