Are there any authenticated stream ciphers that use the same PRF for MAC and cipher?
The Duplex constructions of Keccak (now standardized as SHA-3) work this way.

See:
http://sponge.noekeon.org/SpongeDuplex.pdf

And

http://keccak.noekeon.org/KeccakDIAC2012.pdf

I believe some variant of this is in the process of standardization by NIST, but I haven't seen a draft yet. See:

http://csrc.nist.gov/groups/ST/hash/sha-3/Aug2014/documents/sonmez-turan_sha3_2014_workshop.pdf