From what I have seen:
Serious riders use 20mm or 23mm tires. I have seen 25mm tires used by casual riders or for training. I'll put a 28mm on the rear for off season practice on the road. Many track forks will not take anything over a 23mm tires.
Never seen anyone changing cranks at the track. Generally the shorter ones are better for higher RPM.
What is your goal for this bike? Track only bike? Track bike for the street? Combo street/track?
Back in the day (100 years ago when you road your race bike to work) they actually canted the dropout up a little to be parallel with the wheel at the seat stay – this allowed you to change gears (i.e. take the wheel off and use a different cog) without changing your brake positioning.
It is an interesting idea for a fixed gear road bike, but obviously not something a pure track bike needs.
Think about which bars you will use. Deep drop track bars have a much longer reach than short drop road bars - thus you may need a smaller frame if you are using long reach bars.
P.S. I can't see that picture you posted.