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Does increasing NEDOS, increase the time and memory requirements for the calculation? If so, how does it scale?
(Pertaining only to calculation and not to the time required to write)

Dear satvik_kashyap,

The NEDOS flag is the number of grid points on which the density of states is computed.
The description of the tag NEDOS can be found in the vasp wiki
https://www.vasp.at/wiki/index.php/NEDOS

To store the density of states in the code a grid of length NEDOS has to be allocated. So the memory requirement will
scale linearly with the number of grid points. But note that the memory requirement of this allocation will be negligible compared
to the rest of the code.
To compute the DOS the density of states has to be evaluated at every grid point. The different grid points are independent.
Therefore the computational time will scale linearly with NEDOS. But usually you do not have to worry about the computational time spent in the density of states.

I hope this answers your question.
All the best Jonathan