The problem with a pedestal sink is that it doesn't provide storage. Think about where you will keep extra towels and extra toilet paper?

I agree that you would have no storage, but you could build some shallow shelves on either side of the sink with a ledge below the mirror and it would give the med cab a built in look and provide storage. I would keep it white and bright, as I would on all the surfaces in a small bath.

I have recently done a bathroom with the same layout. Are you demolishing everything and starting again? If you can build a small niche in your shower for shampoos and soaps - super useful.
2. For the cabinet, like you the problem was that the visitor would see it side on, immediately as they walked in, I found the IKEA Godmorgen pharmacy cabinet which has a mirrored side (and interiors) worked brilliantly. As it is all mirror, it brings light into the room and makes the room seem longer as the side reflects the tiles that are perpendicular to it.
The problem may be for you that is is quite tall and I don't know what height your room is. Even though it is deeper, the mirror deflects the light (sadly I haven't taken recent photos to show you how effective it is but here is a similar layout to yours). If you have IKEA nearby worth your while take a visit to see for yourself.

We are not touching the shower at all for now. Just ripping out the floor to put nice tile in and updating fixtures. Toilet area is really deep so I was thinking to either build out a wall behind the toilet to add a door (above the toilet) or just mount a cabinet for the whole width of the space for storage.
This is a first floor bathroom so it will not be used as much as our main bath plus it is near a large walk in pantry so I am not too concerned about the storage.

have you thought of putting shelving over the door all along the wall?