Well, it seems I made some progress
The issue was that the WEP key is set as "HEX" in wifi router while I was putting WEP "passphrase" type.
So now Rune + Pi + Wifi dongle works (even with 24/192 files).
When I unplugged ethernet cable it took ~ 5 minutes to start playing via Wifi and I needed to refresh network connection via RuneUI network settings.
But I have some more questions:
1. Is it good to use WEP or would it be better / more stable / more secure to use WPA? And if WPA which type?
2. Is it ok to use DHCP in Rune network settings or is it better to use static IP address for Wifi connection?
3. Now when my wifi connected Rune audio works (without ethernet cable) I have tried to power it off and start up again (without Ethernet, just Wifi) and ooops... No sound from Rune + Pi + Wifi connection. So I tried to plug ethernet again, power off / power on, connect to Pi via Putty (ethernet IP address works) and do
wicd start
wicd-curses
to configure Wifi again. This works and I can unplug Ethernet cable again.
Long story, short question: What should I do to have Wifi available also after power off of Pi without a need for ethernet connection and configuring wifi after each power on?