That is absolutely right. For me though all the Sennheiser 6xx series does not work so well for orchestral music. Everything is on top of each other.

Actually headphones with more soundstage sound even less than speakers. It is quite counterintuitive, but this weird 2d extended head stage that headphones like Akg701 and others have is even further away from speakers than headphones that have small soundstage like hd6x0. Actually in any headphone if you have crossfeed to go closer to a speaker representation the soundstage will close in.

Look here is an example, the time domain lasts for a ms and the Fourier response extends from 0 to some tens of KHz. Plug it in Matlab and tweak it as you like

% Define time-domain signal
dt = 0.000001; % time step (s)
t = 0:dt:0.001; % time vector (s)
x = cos(50000.*t-0.0004).*exp(-(t-0.0003).^2/0.00006^2); % time-domain signal
% Perform FFT
X = fft(x); % FFT of time-domain signal
f = (0:length(X)-1)/(dt*length(X)); % frequency vector (Hz)
% Plot results
figure;
subplot(2,1,1);
plot(t,x);
xlabel('Time (s)');
ylabel('Amplitude');
title('Time-domain signal');
subplot(2,1,2);
Amplitude=abs(X);
semilogy(f(1:length(X)/20),Amplitude(1:length(X)/20));
xlabel('Frequency (Hz)');
ylabel('Amplitude');
title('Frequency-domain signal (FFT)');

The maximum frequency of a fast Fourier transform is 1 over the sampling interval or the sampling frequency. As shown in this example https://uk.mathworks.com/help/matlab/ref/fft.html

This does not exactly matter as long as the instrument that creates the impulse and the instrument that measures the impulse response are much faster than the system that is under test. In this case a function generator can easily go to 100 KHz so it is much faster than the headphone, also the microphone that measures the response is much faster than the headphone so you are ok.

I do not understand, your comment can you explain? Only thing I am saying is that the impulse response of the headphone in this graph is known to infinity as the assumption that it will continue to be 0 after the end of the plotted data is certainly a valid one. So we can pad with 0s this graph as much as we want. On the other hand the time 0 in this impulse wrong seems to be arbitrary. If somebody can pass me the data of the graph I can certainly do an FFT and get the Freq response.