"We can find two different baskets that have no common fruit on their labels".
True for the case when there are exactly 4 kinds of fruits
False for the case when there are exactly 3 kinds of fruits

Question 2

"There is a basket that can hold all the fruits"
False because it violates Rule 3.

Question 3

Which of the following statement is always true?
1. Any two baskets have at most one common fruit in their labels (True)
2. Number of fruits = Number of baskets (False for the case when there are exactly 4 kinds of fruits)
3. Each basket has exactly two fruits on its label (False for the case when there are exactly 4 kinds of fruits)
4. There is a basket that cannot hold any fruit (False because it violates Rule 1)

Question 4

Which rule does the following example break?
Fruits: apples, oranges and pears.
3 Baskets:
Basket I - apples and oranges
Basket II - apples and pears
Basket III - apples and oranges and pears
The example breaks Rule 1.

Question 5

Which rule does the following example break?
Fruits: apples, oranges, bananas and pears
4 Baskets:
Basket I - apples and oranges
Basket II - apples and pears
Basket III - apples and bananas
Basket IV - oranges, pears and bananas
Actually this is one of the two possible examples for the case when there are exactly 4 kinds of fruits i.e. it doesn't break any rule.