Almost everything burns. Grapes have a lot of water in them, which is why they are so juicy. Things that have a lot of water are hard to burn, because water does not burn. But if you burn something wet for long enough, the water evaporates and then the thing will burn. So with grapes, you have to heat them until the water evaporates, and then they burn the same way something like cloth or wood would burn.

Of course they do. Anything containing carbohydrates will burn. For that matter, almost anything organic will burn.

Grapes have a very high water content, so they may require a little bit longer to ignite than something dryer, like wood. But given sufficient heat and/or time, they absolutely will burn. Once the water has evaporated out, the sugars in them will burn quickly and energetically.

In fact, if you pop some grapes in the microwave, you can make them burn spectacularly - they'll spontaneously create visible plasma.

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Yes Anything with carbohydrates are bound to burn basically. There's a really famous expirement where you have two grapes in a microwave. You expose them to microwaves and they create plasma.