Sean, check with your local codes and with your building inspector. Most codes require a loop in the line to the height of the sink or to the undersurface of the cabinet. For an island application, double cover the codes and loop under the cabinet at the island and do it again at the sink before the disposer connection. Some local codes allow a studor vent but many don't and there is a dispute among plumbers about the effectiveness of studor vents. If allowed still loop the line just in case.
For sewer line connection, use a 45 degree tee pointing in the direction of the flow with the tee rotated so the connection is above the centerline of the sewer line and preferably on top. Use an 1/8 or 1/4 bend elbow going into the tee depending upon where you are making the connection. Look at the other tees put into your sewer line for guidance.
For electric, the diswasher generally needs its own circuit but it can share with a disposer. It cannot share with the 2 (20 amp) appliance circuits required above kitchen cabinets(alternating receptacles are usually on a different circuit). If those 2 wires are hooked to the appliance circuit at the cabinets then don't use it. If not, then check to see if they are 12 guage with another wire for a ground with a 20 amp breaker. Sounds like your 2 receptacles wires don't have a ground and the receptacles should be grounded also. You better rerun a new circuit with 12/2 w ground nm-b sheathed electrical cable and a 20 amp breaker. Ask your building inspector buy he may allow you to hook a general purpose receptacle to the island but then again some inspectors get awful nitpicky. Some places, like chicago, have their own codes that go way beyond the NEC as since the cow kicked over the lantern and started the fire, they require conduit in residential.