Чтобы правильно вставить слова "a few" или "a little" в предложениях, нужно понимать, когда использовать каждое из этих выражений. "A few" используется с исчисляемыми существительными, которые можно посчитать, а "a little" - с неисчисляемыми существительными, которые нельзя посчитать.

Давайте разберем каждое предложение по очереди:

1. Julia ate... rice, she wasn't very hungry.
   В этом предложении "rice" - неисчисляемое существительное. Поэтому мы используем "a little": Julia ate a little rice, she wasn't very hungry.
2. Mike ate... chips, he wasn't very hungry.
   Здесь "chips" - исчисляемое существительное, и мы можем его посчитать. Поэтому используем "a few": Mike ate a few chips, he wasn't very hungry.
3. I have... cousins that speak French, the rest of them only speak English.
   "Cousins" - исчисляемое существительное. Следовательно, мы используем "a few": I have a few cousins that speak French, the rest of them only speak English.
4. She found... cookies under her bed.
   "Cookies" - исчисляемое существительное, поэтому здесь подходит "a few": She found a few cookies under her bed.
5. I need... water to feel better, that's all.
   "Water" - неисчисляемое существительное. Здесь мы используем "a little": I need a little water to feel better, that's all.
6. I want to save... money to buy a present for my mother.
   "Money" - неисчисляемое существительное, поэтому используем "a little": I want to save a little money to buy a present for my mother.
7. Robert gave me... coins to buy a sweater, it is not enough!
   "Coins" - исчисляемое существительное, используем "a few": Robert gave me a few coins to buy a sweater, it is not enough!
8. Ashley needs... sugar for the cake!
   "Sugar" - неисчисляемое существительное, поэтому используем "a little": Ashley needs a little sugar for the cake!
9. My dad says that I have to learn... words in German, because we are going there for holidays.
   "Words" - исчисляемое существительное, поэтому используем "a few": My dad says that I have to learn a few words in German, because we are going there for holidays.
10. Peter saw... girls running across the field.
    "Girls" - исчисляемое существительное, поэтому используем "a few": Peter saw a few girls running across the field.

Таким образом, правильные вставки будут следующие:

• Julia ate a little rice, she wasn't very hungry.
• Mike ate a few chips, he wasn't very hungry.
• I have a few cousins that speak French, the rest of them only speak English.
• She found a few cookies under her bed.
• I need a little water to feel better, that's all.
• I want to save a little money to buy a present for my mother.
• Robert gave me a few coins to buy a sweater, it is not enough!
• Ashley needs a little sugar for the cake!
• My dad says that I have to learn a few words in German, because we are going there for holidays.
• Peter saw a few girls running across the field.