Which river is known as the river of purity and salvation ?

Which river is known as the river of love because of the past times of Lord Krishna on its banks?

According to legend, River Ganga, polluted by millions of people bathing in her, took the form of a black form and took a dip in this river to cleance herself.

Due to sin of this Sage who killed a cow, he prayed to Lord Shiva for a river to be brought down to Earth to absolve his sin. What is the name of the Sage and the river?

The river which was created when the kamandalu of Sage Agastya was tipped over by Lord Ganesha in the form of a crow is......

It was on this river's banks that the vedic sanskrit originated, as well as many other important vedic scriptures.