Can I use my existing patio, or do I need a new base?

The answer to this really depends on how big and heavy your planned installation will be. For smaller mobile and modular units, you may well be able to use the existing patio.  It might be an idea to ask a builder to check if you will have enough support.  In an ideal world you would have a new base designed specifically to accommodate your outdoor kitchen.  If this were to happen then you could run power cables and the drain at the point of installation.

If you use wood you need to make sure that the area around any oven, grill is non-combustible (Concrete, Metal, Marble etc).