Amelia brought pillows.
The person who brought iced tea also brought an umbrella, but no chips.
The person who brought pasta salad also brought chocolate milk.
Noah brought fried chicken.
The person who brought strawberries did not bring plates or pillows.
Liam brought iced tea and chocolate cupcakes.
Matt brought a basket because he initiated the picnic.
The person who brought fruit punch also brought plates.
Amelia brought chips (sour cream and onion flavor), but no fruit punch.
The person who brought mango juice also brought fruit.
Olivia likes chocolate milk.
The board answers:
Amelia: brought pillows and chips (following hints 1 and 9).
Liam: brought iced tea and chocolate cupcakes (following hint 6).
Matt: Bring a basket (as suggested 7).
Noah: Bring fried chicken (as suggested 4).
Olivia: Bring pasta salad and chocolate milk (as suggested 3 and 11).
Now let's look at the drinks and other items:

The person who brought iced tea also brought an umbrella (suggestion 2), so Liam brought an umbrella.
The person who brought fruit punch also brought plates (suggestion 8), so it can't be Amelia or Olivia (who already has other items). This person could be Matt, because Matt doesn't have any drinks or food yet.
The person who brought mango juice also brought fruit (suggestion 10), so Amelia didn't bring mango juice. Olivia didn't either, because she brought pasta salad and chocolate milk. The remaining person is Noah.
Final result:
Olivia: Bring pasta salad and chocolate milk.
Matt: Bring fruit punch and plates.
Amelia: Bring chips and pillows.
Noah: Bring chicken and mango juice.
Liam: Bring iced tea, umbrella, and chocolate cupcakes