1. How to set up a networking in MOL? What is the ideology? Will MOL have separate IP address bound to my card or it will have the same address as my Linux?
2. I use esound and i want to enable sound in MOL. But MOL configuration allows only "oss" and "alsa" option which means it accesses the output device directly. Of course it doesn't work because soundcard is in use by esound. And i don't want to create additional clutter with stopping/restarting it.

It basically fairly simple.... MOL uses tun/tap and NAT to establish a tunnel to your host.
Configuration should be simple as well: just take care that you have dhcpd installed for the perl scripts MOL uses and that you have activated the appropriate section in the configs by removing the '#' before the setting.
Unfortunately I've some problems with sound and MOL as well... neither sound under X nor in MOL (configured nosound). So, I can't help you there, sorry...