On what inherent parameters does the speed of mosfet depend in a SRAM cell circuit?
I assume you are talking about the cutoff frequency ft, defined as the frequency where the current gain of the transistor equals unity.

These formulas were summarized from Semicondutor physics and devices by Neamen:
$$
f_T=\frac{g_m}{2\pi C_{G}} \text{; where $C_G$ is the equivalent input gate capacitance}
$$
$$
g_m=\frac{W\mu_nC_{ox}}{L}\left(V_{GS}-V_T\right) \text{; in saturation}
$$


  What are the main parameters that decide the speed of a MOSFET apart from its intrinsic capacitance?


From the above formulas it can be seen that the cutoff frequency (thus, the maximum speed for the transistor) is dependent on its operating point and dimensions.


  Does the speed depend on the mobility of the charge carriers?


Definitely.

Sadly I cannot help you with 3D IC technology but I would recommend you to give the mentioned book a read, it helps with understanding the main characteristics of transistors.