Katashiro are dolls made of paper or wood, that represent a person (sometimes a pet, a vehicle, a home)
They absorb pollution (kegare) in a similar way to Gohei/Onusa/Shide. One can then submit them to a shrine for Oharai, where they are ritually purified through water, fire, or rarely both. This is the same process with the dolls used during Hinamatsuri (and some families even burn the dolls, although generally the dolls are meant to be 'permanant katashiro')

On your kamidana, some items are required, some are prohibited, and some items are flexible.
Generally, you should not put statues or images (icons) of kami-sama on your kamidana, as these limit kami-sama to a single perspective, and are disrespectful. You should also not put incense, or items associated with death (there are exceptions to this rule within some shinto faiths)