Looking for 3 different Fantasy stories

[skelling]

They are all from the late 80's or VERY early 90's.
The first one was about a lady who was part of a company sent to a primitive world. There she encountered feathered sentient tigers that sing. She impressed them and the story goes from there.
The second one is about a female witch(?) who while riding through a plain is chosen by the local god (a cat?) which says that she is its food.
The third one is a series about a woman from modern time who is transported into an alternate reality to become an avatar to a god. The other books that happen in the series are about her children one of whom becomes an avatar for the goddess Kali(?).

Thank you for any help you can provide.

[KatG]

The first one may be the Chanur series by C.J. Cherryh.