If I take a level 0 or 1 backup of my database does it include everything in my logical log backup tape? Do I need to keep the tape or can I rewrite on it without loosing any vital information? Also, is it imperative to re-run the continuous logical log backup everytime I backup my db?
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.
It doesn't matter the levelsyou make. If possible stick with the level 0 backup. When to change the logical log tape? Doesn't matter, of course before it is full. I always recommend changing at at regular intervals, for example once a week.