No,simply install it and the upright sections of the cabinet will support it,make sure when you are putting it in place that you dont put too much stress on the thinnest part at the back of the sink as this is usually where they will crack. Also check it at the store to make sure its intact. Most of the bath countertops now come with an undermount sink epoxied in place. Get help to lay it on the cabinet
Depends on how you want to mount the sink. It you want a under mounted sink you will need a plywood 'counter' to support the sink. If the sink is mounted on the granite, then the top of the cabinet is all you need to support the granite.
By vainity you mean countertop? Usually the place you buy it from includes the instalation and will take care of this. Sometimes you need to add support inside the cabinets and sometimes not, depends on the cabinets and the thickness of the granite and edging. Best to ask the people you are buying from for advice. If its tile you will need to use plywood.
Most bath room vanities are sized such at the granite counter top doesn't need any extra support unless it is cantilevered. We just had granite counter tops added to our master bath and the 3/4' plywood sides were more than adequate to support the granite. Each vanity was 40' wide and 23' deep with supports for the granite on all four sides. We had undermount sinks installed at the same time. It is best to have the supplier of the granite responsible for that work. They need to get the cutout correct and the placement of the inserts for the supporting screws. That is assuming they are going to use the inserts rather than just epoxy to attach the sink to the counter top. We have a piece of granite on our kitchen island with an 18' cantilevered section on each end. In this case there is a rectangular support for the whole piece of granite made from 1' square steel tubing. This assures that the ends will not break off.
It would be good to do so, as you will be providing a solid support to prevent it from cracking,,, make sure all nails are sunk into the wood, and no splinters are sticking up. A small imperfection can crack the Granite...
