This is possible, but not necessary. A regular hexagon has 3 pairs of parallel lines, making 6 parallel sides altogether.
yes it is
In a parallel circuit there are multiple possible pathways for the current to flow.
It is not possible because a trapezoid has only 1 pair of parallel sides whereas a rectangle has 2 pairs of parallel sides
The slopes will be the same. It is also possible that both parallel lines have no slope defined - if they are vertical.
Yes, series and parallel connection of batteries is possible. When connected in series Voltage increases. In parallel, Current increases but voltage is constant.
It is possible but not necessary for a hexagon to have 3 pairs of parallel sides. In particular, a regular hexagon has 3 pairs of parallel sides.