No! Per code, and for safety, all ground wires must be connected. If this is n older home with 2 wire wiring then you have no choice. I would suggest the house be rewired for the safety of you family.
Sure. For a light you need a fixture to hold the light and the light itself. The light needs to be connected to a voltage supply which you can get from the outlet. In the outlet box you will have a black, white and bare ground wire. Essentially you connect the white and bare wires directly to the light and switch the black wire (hot) through a switch.
Assuming that you want the light switched and the outlet unswitched and the supply voltage is in the switch box you do the following. Run the supply directly from the input of the switch to the outlet. Black goes to the copper colored terminal on outlet, white to silver colored terminal and ground to green screw. The white wires for outlet and light can all be wired together using a wirenut. Do the same for the grounds. Then one side of the switch is connected to the black supply and the other side of the switch to the black wire on the light.
Power into the first outlet and out to all other outlets, black to gold and white to silver screw, ground wires to ground screw. From the outlet closest to the light switch run power from that outlet up to the switch box. Run another wire from the switch box up to the light. In the switch box tie all the whites together under a wire nut and push them back into the box. Tie all the ground wires together and connect that to the ground screw on the switch. Connect the 2 black wires you have left to the 2 screws on the switch. Does not matter which if you only have power in and power out to the light.
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