kashering counters and sinks

Question

We have just purchased an apartment in the Nachlaot neighborhood of Jerusalem. The apartment was owned by a non-kosher Jewish family. We keep Sephardi kashruth. The kitchen counters are some type of synthetic granite material. There is a double sink in the kitchen which are ceramic of some sort. Can we kasher the counters and sinks, and if so, how? Also, there is a dish drying rack in the cabinet just above the double sink. It is actually 2 racks, one above the other. Can we use them for both meat and dairy? What would the restrictions be? Thank you for your help.