How to connect uC to PC using RS232 with minimum number of signals?
It will depend of the software that you're using. 

A) In my case, as I develop my own PC software, I've never used other pins, only RxD, TxD and GND. So, in this case you can left other pins open. This is called as null modem without handshaking



B) Yes (assuming GND is being considered)

C) Again, it will depend of the software on PC side. Some softwares you can configure to not take care of hardware control. Others will require RTS/CTS handshaking, so you can do a null modem with loop back handshaking 



Source of the pictures: RS232 serial null modem cable wiring