102-Square in a square

Let $ABCD$ be a parallelogram. $IG//AB//CD$, $FH//BC//AD$.  Denote as the figure attachment, then show that $KJLM$ be a parallelogram.
Special case:
if $ABCD$ be a rectangle then show that $KJLM$ be a rhombus
If $ABCD$ be a square then show that $KJLM$ be a square,

101-A property of six points lie on a conic

Let $A,B,C,D,E,F$ lie on a conic. Let $H=AC \cap BF$, $I = EC \cap BD$, $K=FD \cap AE$ $O=KI \cap CF$, $N=HI \cap AD$, $P=HK \cap BE$ , Then show that $O,N,P$ are collinear.