It looks like the candle holders we used to use in italy in front of tombs; some of the older ones have similar ones built in the headstones. Nowdays you mostly see big glass and metal boxes to house the plastic-shelled ones or the electic ones.

Candle or incense. Sure. I think someone who grew up Orthodox could say for sure.

I’ve shown this to someone with a religious upbringing and they’ve also said it looks Orthodox, possibly Greek or Russian but they’re not an expert, sorry

Can you open the top? It looks very similar to essential oil burners