Can you list exactly what graphics you need and the dimensions?
For application icon (and possibly file icon, if we want that to be different) as recommended by Microsoft: 16x16, 24x24, 32x32, 40x40, 48x48, 64x64, 256x256.
Additional useful and common icon resolutions are: 16x16, 22x22, 24x24, 32x32, 36x36, 40x40, 48x48, 64x64, 72x72, 96x96, 128x128, 192x192, 256x256, 512x512.
For the larger resolutions (probably 64 or larger) something generated from the same vector graphic would be preferred, possibly even for the smaller resolutions. The smallest resolutions (24 or below at least) may need some per-size hand-tuning though.
I do not think we should be too much concerned with lower colour resolutions in 2017. We probably need to provide 16 colour versions for technical reasons, however I do not think looking particularly good in 16 colours should influence the overall design in any way.
Transparency can (and should) be used for icons where appropriate.
We can generate the required icon sizes from a scalable vector graphics ourselves (SVG format would be preferred in that case, I think, however PDF (like you did provide originally would also work)), the maybe-hand-tuned low-res versions can be in any pixel image format supporting transparency (like PNG).
As for the logo (which could be used as splash screen, about dialog and on the website), I do not think we have any specific requirements regarding size and/or aspect ratio.
In any case, if the design is done with a program that does not use SVG as its native file format, the original file from whatever program you use would also be useful for us to have (in order to ease possible future derivations) in addition to a SVG.