Ok forst off as for the transmitter you aren't going to get very good reception from it. If you want to use FM to input the sound use an FM Modulator which actually plugs inline with your head units antenna connection.
Now for the lines on your screen. Are you powering the screen directly from your cars electrical system or from the computers regulated supply. If its directly connected to the cars system try connecting it to your computers supply.
Now for the whining noise. Thats called alternator whine. The best way to get rid of that is to ground everything very good. This includes the head unit computer power supply and any other audio equipment you have.
Also are you using a DC-DC supply or an inverter?
If you need any more info just post a reply asking for more help