Does it require Python GPIO Library for the working of pySerial ?

Yes, it is possible. You can easily access and manage your Raspberry Pi by using SSH. SSH stands for Shell. Simply connect your raspberry pi to a using ethernet or wifi etc. Then you can easily access it anywhere from the network from your PC. If you are using Linux, you can use its terminal for tha...

You can directly connect 3.3V output of Raspberry Pi to TRIGGER input of HC-SR04. It will detect 3.3V as HIGH LEVEL. But the 5V ECHO output of HC-SR04 should not be directly connected to 3.3V rated Raspberry Pi input.. It may damage it.. So you should use additional voltage dividing resistors to red...