Is this an acceptable authenticated encryption?
This is basically a description of a protocol, I'll just go over the cryptography related points that you've raised.


At least the nonce is missing from the calculation. Just to be sure I would include the entire counter value used in the CTR encryption. 
64 bit of MAC output should be OK, both NIST SP 800-107 Revision 1 and NIST SP 800-38B define 64 bit of hash output as acceptable. See NIST SP 800-107 table 2. If less bits are used additional security proof would be required.
It is possible to go for an AES based MAC instead (AES-CMAC). AES is likely to be faster - especially if encryption is currently not the dominating cost; this depends on the deployed hardware and runtime environment of course.
That's hard to tell without taking the complete protocol into account. Most of the time the symmetric algorithms are not the hard part of the protocol - authentication and key management are much harder parts to get right. This is why choosing TLS should be preferred. 


There are two side channel attacks that are often forgotten when creating an online protocol.


Timing attacks are particularly dangerous, especially during the authentication/session key derivation phase.
Ciphertext length based attacks are particularly dangerous on the application level, including the authentication phase (e.g. of username/password).


Please take both into account when designing any secure transport protocol.