A dwarf "stopping all tasks" when apparently running out of one type of gem is the hallmark of hauling-caused cancellations - they didn't actually run out of gems, one of the extremely stuffed cut-gem bins is earmarked for hauling, making all gems inside inaccessible; and this can happen while the bin's still sitting in the stockpile.
Even worse, such jobs are sometimes picked and dropped before the hauler manages to pick up the bin, so the bin gets blocked and encrusting interrupted, but the errant gem isn't collected. Hauling interruptions will keep happening if new gems are being cut, so
- you definitely should not try to cut gems and encrust at the same time. The pickup of cut gems regularly interrupts and kills the encrustation process.
As for the statue - that's normal operation for encrusting: encrusted items are originally sitting in the workshop, so they're available for further encrusting jobs and of course are naturally the "closest" applicable item for such jobs. If you want many individual items encrusted, you need to issue few different jobs (because an item can't be decorated with the same material more than once) and wait with orders for other decoration materials until the encrusted items have been moved out of the workshop. In addition, you could set up a separate "take"-linked stockpile to pull the decorated stuff into, to make sure undecorated items from the "giving" pile are used instead of adding extra decorations on already-encrusted stuff.
PS:
@below - yes, sometimes items get marked for a job (this isn't displayed on stockpiles, unfortunately) but not picked up, and occasionally, those marks hang around for a long time although no-one's even considering the job. You can clear such jobs by forbidding, then reclaiming the items you suspect (just hover over the bin and hit "f" twice). This forces any sticking haul jobs to cancel and makes the bin available for new jobs (including even more stupid hauling jobs). You can short-circuit gem hauling blockages by temporarily setting the "allowed bins" count on your cut gems stockpile to zero. Every newly stored gem will take up a full stockpile space, but at least haulers won't block your encrusting operations all the time.