I have a topper that doesn't quite match the color of my own hair. Could I dye both the topper and my hair with the same dye (preferably a color close to my own)? Do I need any special products, or just regular hair dye? Anything in particular I need to keep in mind if I try this?

yes, you can do this. If the color is not way off you could just do the ends of the topper and your existing hair where they meet. You can use pretty much any hair coloring product like Lorreal or Clairol. Just mix it and comb it through. Be careful not to color the base.