Re: frequency response
The frequency response does depend on the characteristic of the amplifier. See my previous post, for example.
But, the transfer function is H(s)=A(s)/(1+A(s)B(s))
For large A(s), which is usually the case within the frequency of interest, you can see that the transfer function depends little on the opamp. But if you approach the point where A is not very large, you will see that effect even more pronounced.
In the problem you are referring to (I am not familiar with Razavi's book), the inverting input sees a star configuration, that is, Cin is connected betweeen the node and ground. You need to get rid of it, since it does not "conform" to the formulas you are familiar with. In all the formulas you only care about input and feedback impedances. You can always use transformations like this to make the circuit look like something you can easily analyze.
Now, it may not be obvious, but the second formula does depend on the opamp characteristic, since Gm depends on frequency.