As Simon said you are using p for two different things. You can use the fact that p(1-p) (where 0<p<1) has a maximum value(find it). You can use it to get a bound for your answer.
Write the Newton's laws in the frame of the ground. It is an inertial frame. Write down all the forces(along both axes). Also observe that for every meter the car moves, block A moves by 2 meter.
That is not going to work.What you say is maximum is true only for a=b,if you apply AM GM inequality on a,b.Doing so for 1st 2 expressions give x=140,y=260.
*I don't know the answer*
no you don't have to include no.of moles of solid.
no, it would go backwards,as Qp>Kp.
for (iii) and (iv) read le chatelier's principle.
http://www.chemguide.co.uk/physical/equilibria/lechatelier.html#top
to prove square root function to be bijective you need to specify the domain and codomain of the function.
if codomain is set of real numbers, then its not bijective.
the integrated rate law for 0th,1st,2nd order might help for problem 13.
for q.14 use first two data to find the rate law and rate constant.
then using arrhenious equation and the third data find rate constant at 650K.
use the integrated form of rate law to find the required time.