The BB and cog size questions are directly related to your components.

You'd have to use the appropriate sized BB for whatever crankset you have on the bike.

The largest cog you can have is determined by your derailleur- it depends on how low the upper pulley can rotate downward without rolling on the cog.

The most amount of cogs is determined by your cassette/hub/freewheel. It's also dependent on your shifters- if you've got indexed (clicky) shifters, they should match how many cogs you have. If you're running friction, you can use as many cogs as you can reliably shift to (if your shifter allows it).

The 700C question is determined (mostly) by your frame clearance and the reach of your brakes. If the wheel doesn't clear your brake bridge, chainstay bridge or the fork crown... it just won't go. If your bike has cantilever brakes, they're probably mounted too low to be adjusted up to 700C. If you have sidepulls, you may need to get longer reach brakes.


So the answer to all your questions is "it depends."