The starting point is working out the speed of air through your rotor disk(s). This air starts stationary at some point above the disk, and is pushed down by the disk. The force required to accelerate the air is what lifts a helicopter, and you can modify the usual Force = Mass * Acceleration equation to Force = Mass per second * change in speed to work out the vertical speed of air past the blades.
Note that this approach is independent of blade design, which is why we start with it. It tells you the conditions that you need to design for, based purely on the disk diameter and the required lift.
It also gives you an idea of the top speed, because you can't go faster than the air you're pushing against. (just an idea though, because you're not flying straight up!)
There a more complete guide with equations here
You can also use that change in speed to work out the power required to fly, from the kinetic energy that needs to be supplied every second to the air as it is accelerated to the required speed. It's worth working out the numbers for a few different disk diameters, to compare hovering power (and thus duration) vs top speed.
Most aerofoils stall at around 15 degrees, which sets the limit for the maximum angle of the blades. If you assume they're going to be at that angle, and you have just worked out the vertical air speed, you can multiply by 1/Tan(15) or 3.7 to get the minimum forward speed of the blade.
You can plug that speed into the lift equation for fixed wings to work out the blade area and lift coefficient you need to generated the required lift.
You'll probably find that you don't need anything like 13 blades and a coaxial rotor.
This is really just scratching the surface though. You could do a whole aerospace engineering degree and still not cover everything you have asked for. FWIW, the text book I used was The Foundations of Helicopter Flight by Simon Newman.