No, kings cannot go sideways. They are no different than ordinary checker pieces in this regard. Kings and ordinary pieces must move diagonally.
Of course you can!
in Chinese Checkers, you can move any way you want. Yes, backwards too.
King's corners, Checkers, King of the hill, and King Kong
yes
In checkers, yes
No
You can
Either a king or an ordinary playing piece may jump a king in a game of checkers in the United States of America. But the rules are different in Italy. Specifically, in an Italian game of checkers, only a king is allowed to jump a king.
Yes
no you can't
yes
no