Yes, you will need an electrical outlet. Also make sure to buy the cable that goes from the garbage disposal to the outlet, sometimes they will not come with this cord and it will be an accessory item. You may need to have an electrician install the outlet, you should make sure it is a GFI.
A garbage disposal does not run on batteries so it will either need an outlet or it be wired into the electrical grid in some other manner. You can get an electrician to install an outlet very easily.
Yes, and i suggest that it be on its own line. Also a GFI outlet would be code since it is near water. Check and see if your drains can handle a garbage disposal. Our house is 100 years old and it cannot handle the disposal.