If you have a catalyst from last years festival, that you never started sculpting, can you still use it next year? Or, in the next summer festival, will all my catalysts be gone? And what about the materials or catalysts in progress? Do they disappear after the festival ends?

The latter in both cases, unfortunately (Though every theme is repeated once. That is, the ones from the previous years Summer fest become the following ones Aged themes. But after that, the only way to obtain the themes in question is to look for them using the Advanced pet search and buy pets of those themes from other players.) 8[. I may end up in a similar situation myself, so what Im doing is focusing on the Catalysts for this years themes I have. If I manage to get to the Aged ones, great, if not (with one exception), no big deal, as I already have a pet of each one of the previous years themes I was able to get and currently have Catalysts for.

The other thing you can do is ask other players with available boxes to make some of your pets. The big drawback of that is most of them want you to provide them with the Sculpting materials you want to use on the pets in question, so depending on what those are and how many you need, it can get really expensive. I myself likely wont do that, because I cant really afford to spend the gold ATM (Im saving it up so I can get enough diamonds to buy another stable, which is a far more pressing thing for me, because the one I do have is already full.), but if you want to do that, go for it 8).

All summer fest stuff, tokens, catalysts, materials for catalysts will, presumably, just poof after summer fest is over, so if you have any laying around, it is better to use/sell them now, so other people can use them, because once summer fest is over, no one will.

(I say presumably, because it used to be they disappeared just before the next summer fest, but I don't know whether it will be when the festival is over that they disappear or just before the next one starts. Either way it doesn't matter, because again, they can't be reused after this fest.)

It also doesn't matter whether they are in your inventory or you 'used' them, they will still disappear.