Magnetic flux inducing EMF

Faraday's Law deals only with the time rate of change of the magnetic flux. So no, it doesn't actually matter how big the coil or magnetic field is when you consider solely the change in flux. However, if you are varying the magnetic field passing through a big coil, you will have a greater change in flux than that through a small coil, so the induced EMF would be bigger.

"Faraday's law states that a coil with a larger magnetic flux will have a larger induced EMF, is this true or false?"

False. This is not what Faraday's law states.

"The induced emf is directly proportional to the rate of change of magnetic flux through the coil."

This is what Faraday's law states.

"So, does this mean that it doesn't matter how big the magnetic flux in the coil is?"

Probably yes, depending on what you mean. Put it this way: the emf that you get per turn of coil when a flux of 0.020 Wb drops to 0.019 Wb in a time of 1 ms is the same as the emf that you get per turn when a flux of 0.001 Wb drops to zero in 1 ms. In both cases 1 V.

Faraday's law states that a coil with a larger magnetic flux will have a larger induced EMF, This is false.

'Because Faraday's law states that the EMF of a coil is proportional to the negative rate of change of the magnetic flux through the coil.' Here negative sign shows that the emf is induced.
Thus a larger magnetic flux will have a smaller induced EMF.

So, induced EMF depends upon the amount(how big) of the magnetic flux in the coil.