ad 1) The Vocore2 module of the NANO has lots of MACs (LAN, WLAN) and Meteobridge SW selects one of those to work with.
ad 2) When you want to tell your router to keep giving the NANO a fixed IP, use the one that lists up in your router logs.
ad 3) You should have your NANO keep working on DHCP and give the task to assign a fixed IP to your router.
ad 4) You have tons of chances to make the static IP settings wrong (Gateway, DNS, mask). When you are not 100% up to networking details (and your questions do point me in that direction) just stay with DHCP and use option 3)