Hello, you should not use delay() with MySensors but wait(), which will poll the NRF24 regularly to receive incoming messages.
You are surely right, that using delay isn't normally a good idea for a MySensors program. In my case I only want to implement a passive node to measure temperature and humidity. So my program don't wait for any incoming messages and delay wouldn't be a problem for this reason. But for the final version delay wouldn't be a good solution for another reason: battery life. But I have now a working sleep function for the ATTiny84 which needs only approximately 6µA during sleep.
In the meantime I found the reasons for my problems. My program just uses to much RAM (only 512 Byte on ATTiny84 available), so the stack destroys other variables and the program behaves strange. But I now found a solution for a working passive MySensors Node for temperature and humidity on ATTiny84 with RFM69 radio module and the BME280 as temperature/humidity sensor. I will show my solution here anytime soon, maybe it is of interest for others who try something similar.