When i connect an LED with a 1k resistor to the pin1 on the Arduino, the LED is ALWAYS on
Yes it will be. That is because the normal state of the logic line on a serial port is a logic one. Therefore you will see the LED lit. If you want it the other way round then you must connect the LED and resistor between +5V and the pin1. In that way you sink the current ( as opposed to sourcing it ) and when something is transmitted the LED is lit up. As you had it the LED is turned off when something is sent and it is hard to see any change in a lit LED going briefly off, where it is easy to see an unlit LED going briefly on.
But then it came to my mind: do i need to solder things to the ARDUINO?
Yes, or at least solder things to pin headers that you plug into the arduino.