Yes
yes. A kite is not a rhombus, but has perpendicular diagonals.
no
Impossible. You cannot have an obtuse angle without an acute angle in a quadrilateral.
It isn't possible to know without knowing the shape of the lot. If you could measure the diagonals, then with that information along with the length of each side, it would be possible to say. If you knew the diagonals, then this equation could be used to give your answer: Area = 1/4 X square root (4p2q2 - (a2 + c2 - b2 - d2)2) p and q are the diagonals a, b, c, d are the four perimeter measurements.
A quadrilateral is not necessarily a rectangle. The only time this is not true is in the case of a square on a quadrilateral without four 90 degree angles.
Infinitely many. Any triangle inside a quadrilateral can be divided into two without affecting the quadrilateral but increasing the number of triangles by 1. And then one of those triangles could be spilt into two and so on - without end.
A trapezoid.
Answer is easy with a diagram. Without the picture, very difficult.
There is not enough information. It can be a kite or an irregular quadrilateral without a specific name.
An irregular quadrilateral.
trapeziod
a parallelogram