Point charge between parallel plates
Too late to answer , but would be helpful to other users .

why total induce charges have to cancel charge Q?

Rather than Mathematical answer using method of images and Green's theorem , I'll try to give an intuitive answer of this question .
In 1st Case - A grounded infinite conducting plate and a point charge Q
We know , Charges are induce in conductors due to induction effect but how much charge will induce on the surface towards point charge Q will depend on-
1.proportional to Size of conductor 2.inversely proportional to distance between  charge and conductor
And how much maximum charge can be induced and in which conditions ?
And the answer is obvious if all the electric field emerging from Q ends on induce Charges on plate and for that induce charges on conductor surface (towards Q) must be be -Q
And condition for this to happen is - if
(Size of Conductor /Distance between the conductor and Q) tends to infinity and potential of infinite plate is Zero
Since ,we assume that grounded conducting plate is of infinite size so condition for induce charge equal to -Q satisfy. And electrostatic energy will be stored between conductor and Q only .
In 2nd Case- Two grounded infinite conducting plate and a point charge Q .
Again , since we assume that plates are of infinite size and are grounded  , so maximum charge will be induced but how much ?
This time again all the electric field emerging from Q ends on the both plates, so the sum of induce charges of surfaces(towards Q) should be equal to -Q. i.e
$$Q_1+Q_2=-Q$$ .
And important thing to note that -value of  $$ Q_1 and Q_2 $$  depends on position of Q alone because no electric field emerge from surface of plate 1 and ends on plate 2 because they are equipotential .