I am remodeling a house on a slab, and would like some advise before I call a plumber.

Background for vizualization: There are two bathrooms, and water heater in the middle of the house with the water lines and main vent stack (cast). Almost directly horizontal to that was an existing kitchen with a sink/vent along an exterior wall (approx 25' from the center of the house). I can only assume that the water/waste water lines run under the slab past this kitchen point.
I want to move the sink from the exterior wall into the room about 6 feet to a newly created island.It appears there is a cleanout just south of where I want to place the new sink, but there is another "cleanout" just outside in the yard from the "old" sink location.

Questions: (1) How would I go about locating the drain and water lines running under the slab before I dig, (2) is it generally permissible/advisable to tie the sink in like this and then tie into the "old" sink vent by running new vent under slab, or should I stub up a "U" vent into the island itself?

I know I will need permits, but want to get a good sense of what I "want" before I go to all of the trouble of permits, and spending time with a plumber.

I live in the south, within city limits, on city sewer, slab construction.

Thanks for your advice, comments, or concerns.

--B