ID4 (0xD3): 41 00 93 41
That is your ID. Note that the first byte read is always a dummy e.g.
ID4 (0xD3): xx 00 93 41
You don't say which library you are using. Or describe any of your hardware wiring.
But the registers are being read correctly. Look at the GAMMA entries. You can see whether you have ILI9341 or ILI9341V chip by looking at the power-up values.
Regarding the screen display. I have no idea what library you are using. Or if your initialisation is appropriate.
Note that there a several ILI9341 SPI libraries. And examples that run on Zero, Due, Teensy3.x, STM32, ESP8266, ESP32, ...
If you want to use 5V GPIO, you must convert the logic levels to 3.3V.
David.