Is it possible to cut vinyl using a standard utility knife?
It is possible to use a knife but you you will be better off using a vinyl tile cutter.
If my light fixture is rated for 60w bulbs, can I use a higher wattage if I want the room to be brighter?
No, this is highly dangerous as parts could become too hot and melt, possibly even causing a fire.
I want to hang some shelves but I am afraid of drilling into wiring behind the wall, what is the best way to check?
Use a stud finder with a built-in AC current detector, this will tell you if there any hot wires behind the wall where you are drilling.