A level archive contains all data (0) or changed pages from the higher level (1,2). So all logical logs earlier made are nor required anymore. There are some exceptions. If you make back-up with onbar and do this parallel (so without specifying the -w flag), then the logical log back-up is necessary to synchronize the seperate dbspaces.
Also if you save for example three level-0 backups, then you can overcome a bad media on the level-0 by going to the previous one and continue from there with logical logs.
It is not necessary to restart continuous log back-up after starting a level backup.
Hope this clarifies things a bit,
Rob Prop