Here is how I would write them.
You don't know about cars as much as me. You don't know as much about cars as me // as I do.
It's not as cold as yesterday. Okay in speech, but in writing I'd use It's not as cold as it was yesterday.
I don't feel tired as much as yesterday. I don't feel as tired as I did yesterday.
I wasn't as nervous as usual. Okay. You could also say I wasn't as nervous as I usually am.
You don't know them as
betterwell as I do. (Simple comparative: I know them better than you do.)
There aren't as many people as were (have been) Not sure what you mean here.
My birthday is the same as yours. okay [/QUOTE]