> Can I upload my Hexs via avrdude or via the Arduino-Enviroment to the new board?
You will have to change programmers.txt to add your bit-banging serial port ISP programmer and have to change boards.txt to make that programmer the default for your board. If you can figure out how to do both of those you should be able to use the bit-bang serial interface to upload sketches, assuming it works as expected.
> And can this board use a serial communicationl with the PC via the COM-interface?
No. It can only be used as an ISP programmer to upload bootloaders and sketches. Look at the schematic for the Arduino Single-Sided Serial Board (version 3) to see how to connect your AVR chip to a 9-pin serial port:http://www.arduino.cc/en/Main/ArduinoBoardSerialSingleSided3