#1.
Never. Parallelograms have two pairs of parallel sides. A trapezoid will only ever have one.
#2.
Always. Isosceles Trapezoids are the basic trapezoids. Top and bottom are parallel, legs are equal length and the there are two sets of congruent angles.
#3.
Sometimes. The legs can vary in length depending on the trapezoid. An Isosceles Trapezoid will have congruent legs, but any other trapezoid can have vary leg lengths. For example, the awesome paint picture below shows two legs that aren't congruent.
#4.
Not sure on this. I don't remember the exact definition of a base. If the base is always the parallel side, then the answer is
Always...obviously. However, if the base is just the top and bottom sides, then the answer would be
Sometimes. The next awesome paint picture shows why.