Step 1: Products with oxygen.
Lithium gives the oxide, sodium gives the peroxide and potassium gives the superoxide. So statement A is correct.
Step 2: Magnetism.
The oxide and peroxide are diamagnetic, while the superoxide has an unpaired electron and is paramagnetic. Statement B is correct.
Step 3: In water.
All three give basic solutions, so statement D is correct, while statement C mislabels the products.
Step 4: Answer.
\[ \boxed{\text{A, B and D}} \]