Are you feeding her at mealtimes or is she feeding herself? Maybe you can sit with her during mealtimes and help feed her, encourage her, and have a meal with her so she can see you eating, it may stimualte her appetite.
My son in the past and even now sometimes doesn't really get distracted, but he more or less goes through "picky" stages where he doesn't really eat much of anything. I just do whatever it takes to try and get him to eat. I sit beside him and tell him how yummy my food is and make the sound effects to go along with it
I also will sometimes feed him myself if he doesn't seem interested in eating but I pretend each spoonful is either a car or plane, train, etc. going into his mouth.
As for variety just try to offer only very small amts of each food item, make it colourful, and make it fun eg. small bits of cooked carrots, green beans. I used to mix in cooked veggies with his pasta and he wouldn't even notice. You can even make soups with pureed veggies that way you know she is getting them down her.
Good luck. Hope this helped a little.