Immortal Grapple

If I have played Immortal Grapple during combat, my opponent can play another Immortal Grapple in the same round of this combat?

yes

Why play IG when one has already been played by an opponent?
The strikes are already limited to Hand Strikes?

Well, you from IG get to have a Press which you can use to counterpress against the opponent's...

Also, you might want to cycle so you can fish for a card that you actually need.