There are some excellent ideas here.

Sleepovers are fun. If your daughter has a small handful of friends to invite. They could have facials, manicures, pedicures, put on make up, watch DVDs whilst munching on chips chocolate and pop corn. All depends on what your daughter likes to do

Taking the kids on a scavenger hunt or shopping trip with certain things to buy off a checklist like –
-a small food item you can all enjoy later (this also helps with the food issue for fussy eaters)
-find a cheap lip balm or bath bomb you can then keep – kmart is great for these kinds of things
-something covered in chocolate
the list could be endless, or you could d a scavenger hunt with clues that you have come up with. For my daughter, we also got $1 little coin purses and put in a scrunchie and lip balm and a few lollies, instead of dong a party bag.
re the food – tacos or wraps are often a winner and the kids can add what they like – you put out various bowls with toppings/ingredients. Or you could just do lots of platters with different things like fruit, cold meat, cheese and crackers, mini meatballs etc All those things are great for the kids to pick at throughout the party and can also be eaten as left overs later, so minimal wastage.

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Not sure if you have a boy or girl but my friend had a rainbow theme for her neice. Inexpensive as could just buy any colour and it looked great!

When my boy turned 10yr he invited 4 boys, who got to sleepover. His birthday is in the winter so by 5pm it’s dark. My husband and the boys all with a flash light walked through the reserve/bush to a nearby restaurant where they had dinner (kids prices $10pp including drink & desert). Upon return they watched a movie with popcorn & snacks. In the morning I made a variety as breakfast: pancakes, hash browns, bacon, vegetarian sausages, scrambled egg, croissants, fruits, etc
Simple but the boys had a blast.

Need to look at their interests if you make it about something they love then they will love it.

Can’t help you with the food, too hard when I don’t know the girl and she’s fussy. I was recently at a 16th birthday party and they played the fruit loop game. You have a bowl of fruit loops and a straw and you’re timed to get as many fruit loops out if the bowl into another bowl. You kinda suck up the fruit loops. It was fun to watch

How broad are your tastes? Friday Night Lights, The Walking Dead, and Supergirl all come to mind.