Yes exactly

Yes, it needs several batteries. I'm no longer sure whether these were included in the package. However, it works well. It needs water at least 10cm high for the water to pump through the hose. At first I thought it was broken because the motor was running but the water wasn't coming out. When we added more water to the pool, it worked. My 20-month-old daughter loves playing with it.

No, it connects directly to the tap and works perfectly!

Yes it does

Yes, it needs batteries for the pump.