Does Blockchain.info track IP addresses?

yes it does, see under Account - Settings - Logging

I guess that disabling logging only disables the DISPLAY of logging info on your side.

see https://blockchain.info/privacy:

What we collect

We may collect the following information:

Contact information including email address, skype or google talk username
iPhone or mobile device identifier
ip address
Yubikey or other two factor authentication toke

My name and identifying information is never connected with my bitcoin, is it anonymous?

Not really... See the Bitcoin.org FAQ Generally speaking, I'd say it MAINLY depends on how you get / spend bitcoins. If you pay for something with TC, and give your shipping address, that's your anonimity compromised! Avoiding address re-use gives more anonimity...

How can I keep my bitcoin wallets and usage anonymous?

It all depends on how anonymous you really want to be. For example, do you use Google authenticator? That add to security but certainly decreases anonimity

See also: https://blockchain.info/wallet/anonymity

Will Blockchain.info give up my IP address if "requested" by TPTB?

Sure!

We will not sell, distribute or lease your personal information to third parties unless we are required by law to do so.

(always from their "privacy" page)

Should I be using TOR for all of this?

If you want more protection, yes. But depending on the usage you do of your bitcoin, it might be useless, as you anonimity is already compromised in other ways.