Thanks Kimot. I did use 3,3V voltage as the radio NRF24L01+ is supposed to run on 3,3V only. I did not realise that it affect the crystal frequency. When I now tested with 5V it works perfectly! I will purchase an 8Mhz crystal instead and try it all on 3,3V with a step up booster 1,5 -3,3 to 3,3 V with AA batteries.
Regarding the "broken" pro mini - I must have broken something else too, as after removing the connection in front of the sms led it unfortunately stopped responding to communicate. So I must have destroyed more than just the LED.
Anyway, I am happy I was able to built my own "arduino node" with only the chip, crystal and few capacitors and resistors. It is great to see it working!
Thanks for your help.