Can hyperkalemia and hypernatremia occur at the same time from IV fluid?

Possibly. Electrolyte abnormalities are common in hospitalized patients and can result from multiple factors. They often result from a patient's underlying condition. Intravenous fluid composition could also play a role. You should discuss with your doctor for specific answers in a specific situation.
No, The only commonly used IV fluid containing potassium is deficient in sodium and also contains free water.
Yes and NO. If ivf have Normal Saline and high potassium content, then the answer is yes. But if ivf are half Normal Saline of dextrose in water or other (without potassium) then the answer is no.