Oh, I forgot about a cutting board...
We kind of did the same thing but used a thinner tile that matched our granite and you can put sticky felt on the bottom so it doesn't scratch, we also had a friend make wooden frames around some of them so they looked nice for trivets...you can make matching coasters the same way...but smaller
I didn't make one for this house though, I use a flexible cutting mat for chopping things.
We just picked up our new bathroom vanity top yesterday and the second one has to be custom made for the wonky little sink in that bathroom...so, there is no issue with granite and water. Oh, you can actually get a kitchen sink made from real granite too so water can't possibly be an issue...you have to build up under your sink for extra support and they are quite pricey but they sure look nice!