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#include <SoftwareSerial.h>
#define TX 1
#define RX 2
#define ask 3
#define ER_LED 12

String dataline = "605030";
const byte code = 60;

SoftwareSerial syserial(RX, TX); // RX, TX

void setup() {
  // put your setup code here, to run once:
  syserial.begin(57600);
  Serial.begin(57600);
}

void loop() {
  // put your main code here, to run repeatedly:
  //syserial.println(dataline); //NO
  //syserial.println(28, DEC); //ok for numbers
  
  Serial.println(dataline.length());
  for (int i = 0; i < dataline.length(); i++)
  {
    syserial.print((char)dataline[i]);
  }
  syserial.println();
  //syserial.write(234);
  //syserial.print('<');
  delay(4000);
}

#include <SoftwareSerial.h>
#define TX 1
#define RX 2
const byte ask = 3;
bool com_end;
#define ER_LED 7
#define AC_LED 5


SoftwareSerial syserial(RX, TX); // RX, TX

void setup() {
  // put your setup code here, to run once:
  syserial.begin(57600);
  Serial.begin(57600);
}

void loop() {
  // put your main code here, to run repeatedly:
  while (syserial.available())
  {
    Serial.println(syserial.read());
  }
  delay(100);
}

#include <SoftwareSerial.h>
#define TX 2
#define RX 3
#define ask 3
#define ER_LED 12

String dataline = "605030";
const byte code = 60;

SoftwareSerial syserial(RX, TX); // RX, TX

void setup() {
  // put your setup code here, to run once:
  syserial.begin(57600);
  Serial.begin(57600);
}

void loop() {
  // put your main code here, to run repeatedly:
  //syserial.println(dataline); //NO
  //syserial.println(28, DEC); //ok for numbers
  
  Serial.println(dataline.length());
  for (int i = 0; i < dataline.length(); i++)
  {
    syserial.print((char)dataline[i]);
  }
  syserial.println();
  //syserial.write(234);
  //syserial.print('<');
  delay(4000);
}

#include <SoftwareSerial.h>
#define TX 2
#define RX 3
const byte ask = 3;
bool com_end;
#define ER_LED 7
#define AC_LED 5


SoftwareSerial syserial(RX, TX); // RX, TX

void setup() {
  // put your setup code here, to run once:
  syserial.begin(57600);
  Serial.begin(57600);
}

void loop() {
  // put your main code here, to run repeatedly:
  while (syserial.available())
  {
    Serial.println(syserial.read());
  }
  delay(100);
}

Update :

I changed the pins on the UNO (TX ->2)(RX -> 3), and now i'm getting different numbers again. I must be doing something bad, but I can't understand what.

Serial monitor on whatev b/s:

SySerial monitor on 57600 b/s:

SySerial monitor on 300 b/s:

Serial monitor on whatev b/s:

Monitor with SySerial on 57600 b/s:

Monitor with SySerial on 300 b/s: