Full, incremental or differential backup?
Does this mean, that among these backup pieces there is one incremental backup of a data file or control file?


No, the Backup type is D means it's backup of data files or control file but it's not incremental its full backup(denoted by NULL for INCREMENTAL_LEVEL).

Other backups are differential incremental backup of the backup type D which is base for these incremental backups.


  The difference between this and other databases is that most other databases are backed up incremental level=0. So might there be the difference?


Incremental Level 0 and Incremental Level 1 Cumulative is different types of backup so there is difference. 


  Incremental backups can be either level 0 or level 1. A level 0 incremental backup, which is the base for subsequent incremental backups, copies all blocks containing data, backing the datafile up into a backup set just as a full backup would. The only difference between a level 0 incremental backup and a full backup is that a full backup is never included in an incremental strategy.


For more: RMAN Incremental Backups