URGENT A Level Physics Help

https://www.marlingphysics.co.uk/_files/ugd/b7e24b_af960628b1594af0922b6335e7d1fd29.pdf

MS: https://www.marlingphysics.co.uk/_files/ugd/b7e24b_b6f735fea0564903b90730913e96a5f3.pdf

Question 21 part B, if emf = BANωsinωt and w doubles and B halves then how is the emf not remaining the same / the graph remaining the same?

First of all, you should note that a sinusoidal graph/curve has “2 parts” - amplitude and period.
When the coil rotates twice as fast and the magnitude of the magnetic flux density is reduced by half, the amplitude of the sinusoidal graph/curve would be the same
½BAN(2ω) = BANω
but the period would decrease
(2π)/(2ω) = π/ω ≠ (2π)/ω

would it be fine to think of the whole thing as two separate equations - f = 1/T, double f halved T, and E = NBA/T, halved B and halved T so no effect on E, just an effect on f?

Not sure why do you want to consider 2 separate equations.
You are the one that recognizes that induced emf = BANωsinωt, and now you are “only considering” E = BAN/T (with missing constant).
If both B and T are halved, there is an effect on the induced emf.
The new induced emf is BANωsin(2ωt).

I thought it'd be easier to see that the change in frequency has an effect on both the y and x axis, but the change in flux density only affects the y axis.