Jancy and her husband live in a society with a park in the shape of a quadrilateral \(ABCD\). There are lamp post at the boundary of the park, and an entry gate is at point \(P\), the midpoint of side \(BC\). A path runs diagonally from corner \(A\) to corner \(C\). The gardeners have set up a water sprinkler system, and the four sprinklers are located at points \(P, Q, R, S\), which are the midpoints of the sides \(BC\), \(CD\), \(DA\) and \(AB\) respectively.
Based on the above scenario, answer the following questions:
1. If the the four sprinklers at \(P, Q, R\) and \(S\), what kind of Regular quadrilateral is formed by \(PQRS\)?
2. If the park \(ABCD\) is a rectangle, what kind of quadrilateral is formed by joining the midpoints \(P,Q,R,S\)?
3. If the length of side \(AC\)(the diagonal of the park) is \(30 m\), what is the length of the line segment \(PQ\)?
4. If the quadrilateral formed by the sprinklers \(PQRS\) is a Rectangle, what special property must the diagonals of the park \(AC\) and \(BD\) have?
4. If the quadrilateral formed by the sprinklers \(PQRS\) is a Rectangle, what special property must the diagonals of the park \(AC\) and \(BD\) have?