Q1) Are there any other internal signal monitoring functions such as CX3 PCLK_TP, HSYNC_TP, VSYNC_TP?
For example, RESET, CLK, other operating strobe monitor signals, etc.
Usually, as you mentioned, PCLK HSYNC and VSYNC test points are used for debug. Apart from these, UART lines can be brought out to collect debug logs.
Q2) Are there any test/debug functions/method that users can use to debug FX3/CX3 mounted circuits or circuit boards?
Firmware: CyU3PMipicsiGetErrors() is used to collect MIPI errors (if any) from the MIPI receiver and CyU3PDebugPrint() is used to send those logs via UART. Please see example CX3 firmware in FX3 SDK for the same.