If you really want to use Arduino as a serial/USB converter you have two options.
1. Remove the processor (very carefully)
2. Connect a jumper wire between Reset and Ground. (and not a capacitor as you have now)
For safety upload an empty sketch (as you have done, and the resitor you have is fine for protecting)
But it is cumbersome as you have probably already figured out.
First you need to connect your ArduinoISP with your ATtiny. When you have finished programming, you must remove the programming wires
and then connect other wires to use the Arduino as Serial/USB. If you want to make changes you have to start over.
It is incredibly much easier with Coding Badly's TinyISP - no more fiddling/connecting/reconnecting wires.
You just program your attiny let all wires be where they are, and opens serialle monitor to see your debug text
It's a real relief, it makes programming and debugging of ATtiny's as easy as an Arduino