What meaning of the word "play" is משחק? Does it mean playing a game, playing an instrument, or either?
It can mean to play a game, or to act (i.e. what an actor does). To play an instrument is לנגן.
Does this cover all types of games e.g. cards, board games, tennis or hockey and something like hide and seek?
What about the concept of "playing with someone" or "toying with"? Like a cat with a mouse or one person with another.
Yes, for example אני מנגן בגיטרה = I play guitar. (or: I am playing a guitar).
I said "Are you acting?" and was counted wrong. I thought משחק could also mean acting??
Can it count as playing around like when you prank someone and lie saying something like "theres no school tomorrow" but then youre like "nahhh im playing, we do have school tomorrow"..?
No, for pranking and such the verb used is usually "לסדר" (which also means to get in order)