Can you make a split without adding a mated queen/can a split raise their own queen?
A split can raise their own queen (if they have eggs), but it is better to purchase a mated queen or queen cell from a local bee breeder. Queens raised by a split are reared under the worst possible conditions, are physiologically inferior, and you aren’t taking the opportunity to improve your hive genetics. For a number of reasons, colonies get more aggressive if splits raise their own queens. We always use queen cells that we have reared from breeder colonies so we can maintain and improve our genetics. Cells found in hives can be poorly reared if conditions aren’t good or if you use swarm cells you, are unintentionally breeding for swarming behaviour.
Do you add a frame of pollen or honey into a new split?
Ideally you add both pollen and honey to a new split. Of the two, honey is the most important.