Does the diagonals of a rhombus bisect each other? (Yes/No)

$ABCD$ is a rhombus. Is $\overline{AB}=\overline{BC}=\overline{CA}=\overline{AD}$? Justify.

In a rhombus $ABCD$, is $\angle A=\angle C$? Justify.

In a rhombus $ABCD$, is $\angle B=\angle D$? Justify.

$ABCD$ is a rhombus. Is $\overline{AO}=\overline{BO}=\overline{CO}=\overline{DO}$? Justify.   

$$$ABCD$ is a rhombus. Is $AO=CO$ and $BO=DO$? Justify.