NFS LIFs would need to be migrated, ISCSI LIFs cannot be migrated - you will need to take them offline, but access should continue over the new LIFs due to ALUA.
If you have not tested this functionality inside your environment, I cannot give you assurances that this will be non-disruptive, as it requires network connectivity to be correct, but it usually is - your best course of action would be to setup a test SVM, with new LIFs on both the old and new nodes, create a new datastore and map it, then test the activity with that.
Yes, SVM root volumes will need to be moved to surviving nodes, and this will be non-disruptive.
Hope this helps!