What are the standard sizes/clearances for bathroom elements?
Toilets

The standard side clearance for a toilet is 15" as measured from the centre of the floor flange to the side wall and or cabinet. This measurement is increased to 18" for ADA compliance. I wouldn't go much more then that as you will start to feel like the toilet is floating in the room. The standard distance from the back wall to the centre of the floor flange is 12" for a tank type (10" for flush valve type).

Cabinet Depth

I'm not sure what the standard vanity counter depth is but it would be determined by what is available and what size the sink is.

Corner Shower

Showers come in a variety of sizes. While 36" x 36" is common you can also get 34" x 34" and 38" x 38".

You seem to have a good idea on the spaces needed. Your best bet would be to select the fixtures you want to buy (ones that meet you budget and taste). Then confirm that they will fit in the space. If they do not, adjust accordantly (pick different fixtures or increase the bathroom size if an option).