1. You can use the Cy_TCPWM_Counter_GetCapture() API to read the captured count value.
2. Yes, TCPWMx_CNTy_CC register stores the captured count (x is the TCPWM group number - 0 or 1, and y is the counter number). Please use the API mentioned above instead of direct register reads since PSoC Creator may re-assign the Counter to a different TCPWM address when you make changes to the TopDesign schematic.
3. The logic looks ok to me. However, I'd recommend examining the following code example for component settings and API reference, which documents a similar technique used for frequency measurement:
Please let me know if you have more questions.