regarding your first question:
depending on what management class (TSM_MGMTCLASS) your instance is binded to, will dictate were your logs will be archived. on the tsm server, if the management class has a copy destination of disk, your logs will go to disk first.
typically a disk storage pool has a high and low migration percentage that when reached, will migrate data from disk to tape. rule of thumb settings are:
High Mig Pct: 90
Low Mig Pct: 70
some tsm admins will initiate migration once or twice a day through scripts.