Removing and adding values

The list is \(1,6,10,14,19\).

1. Remove one value so that both the median and range are unchanged.
2. A value \(p\) is instead added to the original list so its mean rises by 3. Find \(p\).
3. A value \(q\) is added to the original list so its median decreases by 2. Find the greatest integer \(q\).