It takes awhile for the pincer grasp to develop effectively enough to get food into their mouths. It was somewhere between 10-11 mo that Tyler got it. Until then, I did what you're doing. I fed him from my fingers, but I'd put finger food out on the tray for him to "practice" with. She'll get it eventually, so keep encouraging her to figure it out herself while still feeding her.
If she doesn't like chunkier food, that's okay. If you want, you can ease the transition by thinning it out with water or mixing it with smooth puree food. If she still doesn't like it, that's okay! Tyler never ate any of the Stage 3 foods, and that was fine by me.
Using a spoon on her own...not for awhile yet. I've heard of some babies starting to at 1 yr, but most that I know of don't get it until well after their first birthday. As with finger food, keep giving her opportunities to learn, and she'll get it in her own time! HTH!