Ok, i have some rather interesting news...
So, i still don't get any responses in the Serial Port yet, and tried this:
void loop() {
if (FingerprintReader.available()) {
Serial.print(FingerprintReader.read(), HEX);
Serial.print(" ");
digitalWrite(13, HIGH); // Just to see if "FingerprintReader.available()" ever becomes true
}
digitalWrite(13, LOW);
}
And apparently "FingerprintReader.available()" never becomes true (or if it does, is true for such a short time, that you can't even see the LED flashing :))
I think maybe the NewSoftSerial library doesn't work right with me, because the Examples seem not do really do what they are supposed to do either...
If i upload this Example:
#include <NewSoftSerial.h>
NewSoftSerial mySerial(2, 3);
void setup()
{
Serial.begin(57600);
Serial.println("Goodnight moon!");
// set the data rate for the NewSoftSerial port
mySerial.begin(4800);
mySerial.println("Hello, world?");
}
void loop() // run over and over again
{
if (mySerial.available()) {
Serial.print((char)mySerial.read());
}
if (Serial.available()) {
mySerial.print((char)Serial.read());
}
}
all i receive is "Goodnight moon!", and then nothing... Is that supposed to happen (when nothing is hooked up to the Arduino)?
Anyhow that is not the Interesting part yet!
Then i tried uploading this Script:
#include <NewSoftSerial.h>
byte RequestConnection[] = {
0x7e, // Start Character
0x00, 0x00, 0x00, 0x01, // Command = 1
0x00, 0x00, 0x00, 0x00, // Param1 = 0
0x00, 0x00, 0x00, 0x00, // Param2 = 0
0x00, 0x00, 0x00, 0x00, // Data Size = 0
0x00, 0x00, 0x00, 0x00, // Error Code = 0
0x00, 0x00, 0x00, 0x01 // Header Checksum = 1
};
byte VerifyFp[] = {
0x7e, // Start Character
0x00, 0x00, 0x00, 0x11, // Command = 1
0x00, 0x00, 0x00, 0x00, // Param1 = 0
0x00, 0x00, 0x00, 0x00, // Param2 = 0
0x00, 0x00, 0x00, 0x0B, // Data Size = 0
0x00, 0x00, 0x00, 0x00, // Error Code = 0
0x00, 0x00, 0x00, 0x1C // Header Checksum = 1
};
byte IdentifyFp[] = {
0x7e, // Start Character
0x00, 0x00, 0x00, 0x12, // Command = 1
0x00, 0x00, 0x00, 0x00, // Param1 = 0
0x00, 0x00, 0x00, 0x00, // Param2 = 0
0x00, 0x00, 0x00, 0x00, // Data Size = 0
0x00, 0x00, 0x00, 0x00, // Error Code = 0
0x00, 0x00, 0x00, 0x12 // Header Checksum = 1
};
byte DeleteFp[] = {
0x7e, // Start Character
0x00, 0x00, 0x00, 0x22, // Command = 1
0x00, 0x00, 0x00, 0x00, // Param1 = 0
0x00, 0x00, 0x00, 0x00, // Param2 = 0
0x00, 0x00, 0x00, 0x0B, // Data Size = 0
0x00, 0x00, 0x00, 0x00, // Error Code = 0
0x00, 0x00, 0x00, 0x2D // Header Checksum = 1
};
byte RegisterFp[] = {
0x7e, // Start Character
0x00, 0x00, 0x00, 0x33, // Command = 1
0x00, 0x00, 0x00, 0x00, // Param1 = 0
0x00, 0x00, 0x00, 0x00, // Param2 = 0
0x00, 0x00, 0x00, 0x1B, // Data Size = 0
0x00, 0x00, 0x00, 0x00, // Error Code = 0
0x00, 0x00, 0x00, 0x4E // Header Checksum = 1
};
NewSoftSerial FingerprintReader(2, 3); // Use pins 2 and 3 for serial I/O to reader
void setup() {
pinMode(13, OUTPUT);
Serial.begin(9600);
FingerprintReader.begin(9600);
delay(100); //I added this because of Nick Gammons reply (but the same Script without it seems to do the same, so i don't know if it really does anything)
for (int i=0; i<(sizeof RequestConnection / sizeof RequestConnection[0]); i++) {
FingerprintReader.print(RequestConnection[i], BYTE);
}
delay(500);
for (int i=0; i<(sizeof IdentifyFp / sizeof IdentifyFp[0]); i++) {
FingerprintReader.print(IdentifyFp[i], BYTE);
}
}
void loop() {
if (FingerprintReader.available()) {
Serial.print(FingerprintReader.read(), HEX);
Serial.print(" ");
digitalWrite(13, HIGH); // Just to see if "FingerprintReader.available()" ever becomes true
}
digitalWrite(13, LOW);
}
just to see if the Fingerprint Reader maybe reacts too the IdentifyFp, and amzingly first the Green and Yellow LEDs on the Shifter blinkt after each other, then (after the 500 milliseconds) only the Green LED blinkt and the Background lights on the Fingerprint Reader turned on, and after a while the Background lights turned off, and the Yellow LED on the Shifter blinkt.
So i guess the Fingerprint Reader reacted to the IdentifyFp and then after a while sended his results back... So i guess that is a big step?!
Anyhow, the Fingerprint didn't react to the VerifyFp, DeleteFp or RegisterFp. It didn't even send anything back... Since i just copied the VerifyFp, IdentifyFp, DeleteFp and RegisterFp from troublebuble's older reply, i tried too look in the Serial Interface PDF if the VerifyFp, DeleteFp and/or RegisterFp maybe had any kind of error, but i guess i'll stil have to learn how to read that, so i don't if there are any errors
(sorry)
Well i guess, now i only need to find out why the other commands don't work, why the Serial Port is allways empty, and i guess a also need to figure out how to read the Serial Interface PDF so i know what the responses from the Fingerprint Reader mean (that is when i finally get responses :)).
Well, i'll try to understand the PDF then... 
Thanks for all the Help you all gave me 'til now!
Hopefully some day i'll have a chance to help one, some, or all of you with something too...
P.S. @johnwasser, just for the Record, the Fingerprint Reader also reacts to the IdentifyFp command when i try it without first sending the Request Connection command. (no offense or anything, just a little friendly correction) 
@Nick Gammon i only have VCC, GND, TX and RX connected (on the Fingerprint Reader) so i guess that won't be a problem... 