I am not sure about why the TX isn't working, I am guessing that is more code related. As far as I know, the TX1/RX0 pins run off of Serial1 not Serial. However, and just to double-check, if you want 5V out of the pin between RST and A7 you can only power the board through the USB and you have to solder between the two pads directly above the pin. If you power the board through the VIN pin it doesn't output the 5V.
Here is the extract from one of the IOT pages:
5V on that pin is available only when two conditions are met: you make a solder bridge on the two pads marked as VUSB and you power the NANO 33 IoT through the USB port. If you power the board from the VIN pin, you won’t get any regulated 5V and therefore even if you do the solder bridge, nothing will come out of that 5V pin. The 3.3V, on the other hand, is always available and supports enough current to drive your sensors. Please make your designs so that sensors and actuators are driven with 3.3V and work with 3.3V digital IO levels. 5V is now an option for many modules and 3.3V is becoming the standard voltage for electronic ICs.
I have attached an image that I pinched from this post.
Sorry if that is a bit of a surficial answer. Hope it helps!