See the diagram.
PQ is parallel to RS in the trapezium. Given that A is mid point of PR and B is midpoint of QS. Let C be midpoint of PS and D be the midpoint of QR.
CB is line joining midpoints of two sides of the triangle PQS. Hence, CB is parallel to PQ and also PQ = 2 * CB.
Similarly, in triangle PRS, CA is parallel to RS, and RS = 2 * CA
Rs = 2 (CB + BA) = PQ + 2 BA
AB = 1/2 * (RS - PQ), we assumed that RS is bigger than PQ.
If PQ is longer then RS, then it will be AB = 1/2 (PQ - RS)
For the question 2 :
We don't know about the locations points L, M, P and Q, You need to enclose a diagram.