The best thing to do with carvings and ornaments is to appreciate them without unnecessary handling. Apart from the occasional cat or earthquake it is usually human error that causes breakage. As long as they are stable or well supported they will generally outlast any human. 

An occasional wipe-over with lightly soaped water followed by a rinse will keep your stone carvings and ornaments looking good. Cleansing them will also bring out their best.

A final buff with mineral oil will keep them in pristine condition – be aware that vegetable oils tend to leave a residual stickiness that will attract dust and grime.