From my experience the past year (playing and reading the forum) at least once or twice an event repeated from before I started playing. People in the forum were disappointed that they didn't get to reuse things they had already accomplished. Although the game makers do reuse pictures of food/decorations (sometimes renaming, sometimes making them available to gem purchase) it seems they are trying to stay away from reusing 'new' appliances specific to events. I've never had an event appliance become useful for another event.
That being said, I use my Campfire Stove and my Snowy Oven almost all the time to earn coins easily. My campfire stove makes a great Yeti Spaghetti and the Snowy Oven has Holiday Tree Rolls, both produce lots of coins for underused ingredients. I sometimes pull out my Ghostly Stove to make Octopus Dip (which looks adorable served). Both the Snowy Oven and Ghostly stove have special cooks which appear in my kitchen if their appliances are out and in use. Note these special appliances often don't give things that the regular appliances do--like no stamp drops, no appearance in Cruises.
Gems only go away when you spend them!
Gem recipes aren't limited! That is, at this time I believe there are up to 3 gem stoves. Cruise recipe rewards have come up on Celebration Stove and Jubilee Oven. The Festival Stove can be purchased for 1600 gems and comes with a gem recipe. (I haven't bought it, so I don't know if more recipes have come on that stove yet)