The problem is, that I'm unable to establish any kind of connection.
First I tried to connect it using software serial ports, but I got nothing. Then I tried hardware serial and got the same results. I tried simple example sketches I found on the Internet. I couldn't connect to it.
Serial.available() returned false
Even if i just connect it to pover and ground, I'm unable to see them on my phone(and any other phone).
Also the LED is blinking fast. I can also start it in AT mode when I hold the button on start, because the LED then blinks slower, but either way, I couldn't get connection.
I would be very grateful for any help.
There is no "either way" If the LED is flashing fast, you will never get a connection. If it is slow, the phone should be able to sniff for it. This is a phone procedure done in phone settings. This presupposes the phone is Android and your Bluetooth really is an HC-05.
You might find the following background notes useful.
In the document, I keep reading, that it should be ready "out of the box".
If i connetct it to D0 and D1 pins. Should this code work in a sense, that if the module could communicate with PC, it will write to the Seerial monitor Available?